Jeremy Peat, who has served as a member of the BBC Trust, claimed if Scotland left the UK a deal would have to be done to ensure this.
He said otherwise digital television services could potentially be "cut off" just over the border "so essentially there could be a removal of access for the great majority to that television".
The Scottish Government's White Paper on independence states that "Scottish viewers and listeners should continue to have access to all their current channels" and also sets out that there should be "no additional cost to viewers and listeners as a consequence of independence".
Culture Secretary Fiona Hyslop last year insisted viewers north of the border would be able to watch the same TV programmes they currently enjoy after independence without having to pay a higher licence fee.
But Mr Peat told MSPs on Holyrood's Education and Culture Committee: "I don't think there can be the presumption that access would continue on a free and unfettered basis to all services."
He was questioned by the committee on access to BBC services post-independence, with Liberal Democrat MSP Liam McArthur asking: "What is your assessment as to what is likely to happen in the event of a Yes vote?"
Mr Peat told him: "So far as access to BBC services is concerned post-independence, my understanding is DTT (digital terrestrial television) could be cut off close to the border."
While he said there "maybe some marginal overlap" with viewers just over the border able to access services, he added that "essentially there could be a removal of access for the great majority to that television".
Mr Peat continued: "Already so far as the iPlayer is concerned and the web is concerned, for countries out with the UK there is a requirement to pay for access and a somewhat different service is provided.
"I would assume that the starting point again would be that those services would be available to Scotland as an independent nation in a different way from the way they are at the moment, for payment, and potentially a different service."
Mr Peat said viewers in Ireland had "access to the majority of BBC services", but went on: "I think the phrase that is used is that it is on a commercial basis."
BBC Scotland currently provides programmes that are broadcast across the UK on the BBC network, and the White Paper proposes an independent Scotland would set up a Scottish Broadcasting Service (SBS) which would enter into a formal relationship with the BBC so this would continue.
This relationship would mean current BBC services would continue in an independent Scotland, according to the White Paper, which states: "Current programming like EastEnders, Doctor Who and Strictly Come Dancing and channels like CBeebies will still be available in Scotland."
But Mr Peat argued it was "very difficult to determine what happens in advance" as he told MSPs the deal set out in the White Paper "strikes me as an arrangement that would require a great deal of negotiation".
He added: "I understand the principle but I think there is an awful lot of issues to be discussed and debated before such an arrangement could be implemented."
He continued: "I have no idea what the outcome of negotiations would be, I was not saying services would be blocked, what I was saying was DTT could be blocked.
"In the only example I have looked at, which is Ireland, and I looked at it very briefly, there was a commercial arrangement before the access was provided.
"The deal that is set out is extremely attractive to Scotland if it can be negotiated and implemented, but I am simply saying it is not a deal that can be deemed done until negotiations and discussions have taken place."
A Scottish Government spokesman said: "Viewers across Scotland would still be able to watch all the BBC's output post-independence, just as they do now. The BBC is watched, as live, in Ireland, the Netherlands and Switzerland, so it makes no sense to suggest that an independent Scotland would be uniquely blocked.
"The fact is, Scottish licence fee payers have contributed to the BBC and would be entitled to a reasonable share of that asset following independence.
"With independence, Scotland will establish a Scottish Broadcasting Service (SBS) which will operate on TV, radio and online, funded by the licence fee. The SBS will seek to work in joint venture with the BBC to mutual benefit. This approach would be in line with the Edinburgh Agreement's commitment by the two governments "to continue to work together constructively in the light of the outcome, whatever it is, in the best interests of the people of Scotland and of the rest of the United Kingdom".
Viewers and listeners would continue to receive the programmes and channels they currently enjoy, but with significantly more programmes being commissioned and produced in Scotland."