Around 150,000 people could see their pay increase in the event of a Yes vote in the referendum, according to the SNP.
The party has said it would set up a commission in an independent Scotland to consider a new minimum wage that would rise at least in line with inflation.
Its analysis found that around 150,000 Scots, or just under 7% of the workforce, will be earning the UK national minimum wage in October, when the rate is due to increase to £6.50.
The wage had failed to keep up with the cost of living since 2008, the party said.
Christina McKelvie MSP, convener of the SNP Parliamentary trade union group, claimed a Yes vote would ensure low-paid workers "earn a fair day's pay for a fair day's work".
She said: "Scotland is one of the richest countries in the world - and yet the latest figures show that the number of people living in poverty is on the increase, with a million Scots now living below the bread line.
"We know one of the key drivers of poverty is earnings - which is why we would use the powers of independence to set a Scottish Minimum Wage guarantee. A minimum wage that rises - at the very least - in line with inflation.
"The Scottish Government is already using the limited powers it has to take steps to help those on the lowest incomes - such as supporting the Scottish Living Wage of £7.45 per hour. But with independence we would have improved wages for all our workers, not just those under the responsibility of government."
The SNP added that if inflation increases had been introduced five years ago, low-paid Scots would have been up to £675 better off.
An expert group set up by the Scottish Government to examine welfare under independence has recommended that the minimum wage be brought up to the same level as the living wage, which is £7.65 an hour.
Deputy First Minister Nicola Sturgeon has said the Government would ''look closely'' at the proposal.
Labour's finance spokesman Iain Gray said: "If the SNP were serious about helping the low paid then they would have supported Labour amendments to the Procurement Bill on the living wage. This is just more vague promises of jam tomorrow."
A Better Together spokesman said: "People won't be fooled by this. They know that the minimum wage was introduced by the UK Government and they know that the best way to secure the brightest future for working families in Scotland is to pull and share our resources across the whole of the UK.
"It is clearer than ever that the nationalists will do anything to get people to vote for independence."