The First Minister described the NHS as being a "fundamental part of Scotland's national identity" as he accused successive Westminster governments of having "scorned and betrayed" its founding principles of providing care free at the point of need.
The Scottish Government has already set up plans for a written constitution to be drawn up if the referendum on September 18 results in a vote for independence.
SNP ministers advocate the document should enshrine the NHS, protecting it from the "privatisation by stealth that has befallen the NHS England".
They also argue the constitution could ensure that NHS services which are provided free today will continue to be provided without charge in future.
Mr Salmond said: "Nye Bevan's founding principles for the National Health Service was for an institution owned by the people, which ensured that all have access to the highest attainable standard of health services, free at the point of delivery, based on clinical need and not ability to pay.
"For me that is not a simple a matter of policy, it's a fundamental part of Scotland's national identity.
"In England, despite the protest of many, the NHS is being eroded and the founding principles handed down by Bevan have been scorned and betrayed by successive Westminster governments.
"It's now well understood that voting Yes will allow us to protect Scotland's NHS from the threat to budgets here as a consequence of the cult of austerity and privatisation being forced on the NHS in England.
"But protecting the budget of our health service is only the first step.
"With independence we have the golden opportunity to enshrine Bevan's founding principles for our National Health Service in the written constitution for Scotland - publicly-owned, clinically-driven and freely-delivered equally for all - a guarantee that not only will the NHS be kept in public hands, but that the services that are free to access today will be free to access in the future."
Mr Salmond went on: "Constitutional protection for the NHS is our promise to generations yet to come that in the Scotland we seek, no-one will be denied medical aid because of lack of means.
"The NHS is at the heart of our nation, and I want it to be at the heart of our constitution."
He was speaking as a new survey suggested three out of five doctors in Scotland are planning to vote against independence.
Research by the BMJ found 60% of medics who were questioned on the issue in a snapshot survey carried out by the publication said they would be voting to keep Scotland in the UK.
A third (33%) of the 311 doctors who took part in the research plan to vote for independence, with 6% undecided and 1% not planning on voting.
But Dr Willie Wilson, of the pro-independence group NHS for Yes, said the BMJ research was based on a small sample size and increasing numbers of health workers believe Scotland should leave the UK in order to protect the health service.
Of the 2,297 doctors in Scotland the BMJ survey was sent to, 14% responded, including 148 hospital doctors and 125 GPs.
Dr Wilson said: "This is a small sample and our experience, having talked to a very much larger number of people in the medical and healthcare professions, is the opposite.
"That's because increasing numbers of people - both those who work in the NHS as well as those who depend on it - know that only a Yes vote can protect our public health service from the impact of Westminster budget cuts and privatisation which is running rampant in the NHS in England."
Labour MSP Jackie Baillie, speaking on behalf of the pro-UK Better Together campaign, said: "This survey shows that people working in our NHS know that the best way to protect our health service is to stay part of the UK."
She added: "By pooling our resources across the UK, Scotland's NHS gets almost 10% more spending per head of population than in England. That means that yearly health spending is around £200 per person higher than the UK average. This is a clear positive benefit of staying in the UK."
Scottish Liberal Democrat leader Willie Rennie said claims from the First Minister and the Yes campaign that the NHS will be under threat if there is a No vote are "dishonest".
Speaking at a meeting of Better Together activists in Glenrothes, Fife, Mr Rennie insisted the principles of the health service are "unique and enduring".
He added: "For the Nationalists to claim that they are under threat is dishonest, desperate and disgraceful. It is also factually wrong.
"Despite the financial pressure of the global financial crisis, the NHS budget has been protected and NHS funding in England is now £12.7 billion higher than it was in 2010.
"Private sector involvement in England's NHS is paid for with public money, meaning that the cash equivalent is protected for Scotland - and the Scottish Government can spend it however they see fit."
Mr Rennie said that with just weeks to go until the referendum, "the SNP has suddenly started to pretend that funding is in doubt".
He claimed: "Standing on street corners, dripping poison about the NHS into the ears of passers-by, is a sign of just how desperate they are becoming. But it's no surprise.
"People are worried about the impact independence would have on their public services - the Nationalists know this and they are trying to distract attention with bluster and lies."