Mr Alexander said any threats by Scotland's First Minister Alex Salmond to refuse to take a share of the debt as a result of the UK Government's rejection of a currency union could have a "huge effect on mortgages and businesses".
The Chief Secretary was appearing at Holyrood's Economy Committee to give evidence on Scotland's economic future post-2014.
Chancellor George Osborne has already warned that even if a new Scottish state accepted its share of UK debt, it would have to pay an ''independence premium'' to borrow from the markets.
This would mean an extra £1,700 a year for the average mortgage-payer, Mr Osborne said.
Mr Alexander told the committee that new independent analysis from Jefferies investment bank suggests this figure could rise considerably if a share of debt was refused.
"In the event of a default, of a refusal to accept debt, one bank, Jeffries investment bank, has done the only detailed estimate out there - they have suggested that under those circumstances there would be a premium of more like five percentage points in that default scenario," Mr Alexander said.
"If you run that through the calculator in terms of how that gets passed on to the real economy... it would have a huge effect on mortgages and businesses.
"Assuming a 75% pass through from bond rates to mortgage rates would be an extra cost of about £5,200 on an average mortgage cost in Scotland.
"None of these things are certain, but you see the range of financial risks that come with borrowing under an independence framework."
Mr Alexander said: "The idea that you would start your life as a new nation state like that would be cutting off your nose to spite your face.
"The expectation within the markets is that part of the proper process of independence is taking on a fair share of the debt, and in the end market credibility and confidence is based on the perception that a country is willing to take on its financial obligations."
Mr Alexander's warning over elevated interest rates came as he announced that the Scottish Government is to be given the power to issue its own bonds.
He said Jefferies' estimates were based on what would happen to bond yields in the event that Scotland did not take a share of UK debt.
The Chief Secretary also told committee members that continuing to state that there would be a currency union was "not a credible position to take".
He said: "I really don't think that people should accept this line that somehow this is a bluff that will change after the referendum.
"The idea that any of us would have chosen to make the statement we did, based on the rigorous analysis that was published, and plan to change our minds a few months later, I am afraid, is just a fantasy.
"You should treat what is being said in respect of a currency union as being definitive."
He said an independent Scotland, in effect, would face two choices - either to establish a separate Scottish currency, as a replacement for sterling, a staging post to joining the euro, or as a way of "locking in" an exchange rate with the pound, or opt for "Sterlingisation" outside a formal union.
"The advantages of a Scottish currency would be the power to set your own interest rates, the ability for your exchange rate to fluctuate... but the weaknesses of that option would very much be the damage to trade, and the extra barriers which would be created between Scotland and the rest of the UK," he said.
Mr Alexander warned that Sterlingisation could be "very dangerous", as it would leave Scotland without a lender of last resort, which would be "critically important" given the size of its financial sector.
"It would be enormously helpful for people in Scotland to understand what is the plan, because otherwise we are being asked to follow a proposal for independence with no route map, and no sense of what the destination is."
Deputy First Minister Nicola Sturgeon later dismissed Mr Alexander's claims that mortgage costs would rise in an independent Scotland.
She told the committee there was "not a scrap of evidence that would be the case".
Ms Sturgeon added: "There are examples of other small European countries that have lower mortgage costs than people in Scotland as part of the UK right now."
She also argued that the "mortgage rates that people pay are based on partly the base rate of the Bank of England and competition".
Meanwhile, Scottish Finance Secretary John Swinney warned that failure to agree a deal with an independent Scotland on the division of liabilities and assets - including the pound - could result in the remainder of the UK having to pay up to £5.5 billion more a year in debt servicing costs.
He said that would be the equivalent of increasing income tax by one penny for people in the rest of the UK.
Mr Swinney stressed that the Scottish Government's independence White Paper had set out for UK debt to be shared if there is a Yes vote in the referendum.
But he told the committee: "If we follow the logic of the Treasury's position, the Treasury is walking into the payment of an extra £4 to £5.5 billion a year in debt interest charges to sustain and up to an extra £130 billion of debt.
"Under the proposition we have put forward, an independent Scotland would be quite happy to pay, as part of negotiated arrangements which would include participation in a sterling zone."
Mr Swinney said the Treasury had "set out the United Kingdom would be the continuing state, and as a consequence of that situation would essentially have exclusive access to the role and the responsibilities of the Bank of England and the sterling currency".
He added: "If you follow that argument to its logical conclusion then the United Kingdom assumes entire responsibility for the liabilities of the United Kingdom. What that would mean is that the United Kingdom would be taking on an additional share of debt that could be supported by an independent Scotland, of up to £130 billion.
"That would result in debt servicing costs of the rest of the United Kingdom increasing by between £4 billion and £5.5 billion each year, which would be the equivalent of increasing income tax by one pence in 2016-17."
The Finance Secretary insisted that was the "logical conclusion of the position the United Kingdom Government has adopted by arguing for successor state status".
Mr Swinney told MSPs: "If the UK Government wishes to have its cake, it cannot eat it as well."
He argued: "If one's position is to take all of the assets, one's position must be to take all of the liabilities."
The alternative to this, he said, was the "responsible approach" put forward by the Scottish Government for the "fair distribution of assets and liabilities", adding that "out of that would come an agreed position on the continued use of sterling and the establishment of a currency zone".
He said adopting this approach would see "an independent Scotland taking and fulfilling its obligations in relation to debt repayment".
Responding to Mr Alexander's comments on the consequences of failure to accept a share of debt, a spokesman for Mr Swinney said: "Danny Alexander is talking nonsense, and this is another of the ridiculous, overblown and transparent scare stories that are doing such damage to the No campaign.
"For a start, our policy is that an independent Scotland should agree to finance a fair share of debt which will remain legally that of the Westminster Treasury - as they themselves confirmed last month - on the basis that Scotland gets a fair share of both assets and liabilities.
"The Treasury has accepted all the debt will be legally theirs because of Westminster's argument that the rest of the UK will be the continuing state - so by definition it is impossible to default on a debt that is not legally yours."