The Low Pay Commission has recommended a 3% rise in the minimum wage to £6.50 from October, Vince Cable has revealed.
The Business Secretary said the figure, if accepted by the Government, would be the first real-terms increase since 2008.
After disclosing the recommendation to a parliamentary committee, Mr Cable said: "It is faster than inflation and that is the first time in six years that has happened."
The LPC has suggested that the level for apprentices should rise by 2%.
The recommendation - revealed by Mr Cable to a committee discussing minimum wage regulation changes - is below the increase from £6.31 to £7 that had been floated by allies of Chancellor George Osborne last month.
"It is not dramatic, but it is important," Mr Cable said. The LPC had balanced "fairness against the risks to employment" if the level was set too high, he added.
Mr Osborne said last month that the economic recovery meant "Britain can afford an above-inflation increase in the minimum wage so we restore its real value".
Treasury analysis has suggested that increasing the National Minimum Wage to £7 by 2015-16 would only have a minor impact on unemployment.
"We hope this is the first in a series of bolder increases that will give real help to the low paid, and not just a pre-election boost."
Asked whether the Prime Minister was satisfied with the LPC's recommendation, David Cameron's official spokesman said: "Three per cent would represent a real-terms increase and I believe that the LPC has signalled that this could be part of a process by which the value is restored to what it was before the great recession.
"That is entirely in line with the position the Chancellor was setting out earlier in the year."
Asked whether the rise to £6.50 will now be implemented, the spokesman added: "The LPC submitted its recommendation today. They Government will want to take time to consider it."
Shadow business secretary Chuka Umunna said: "This announcement exposes the comments George Osborne made just weeks ago about a £7 minimum wage as misleading and empty rhetoric.
"Labour said last year that we need to see above-inflation rises in the minimum wage to restore the value lost over recent years. That's why we welcome the Low Pay Commission's announcement and have committed to strengthening the minimum wage so that its value is properly restored."
Adam Marshall, executive director of policy at the British Chambers of Commerce, said: "As the economy continues to improve, businesses agree that the minimum wage must rise.
"While the Low Pay Commission's recommendation appears to be slightly higher than many employers had hoped, it represents a reasonable compromise."
Dr Marshall added: "Ministers must follow the Low Pay Commission's carefully-evidenced recommendations, rather than ignore their independent advice and take a purely political decision".
And above all, they must work hand-in-hand with business to raise productivity and skills in the workplace - which are the keys to higher wages for all in the future."
Tim Thomas, head of employment policy at manufacturers' organisation EEF, said: "Whilst economic data continues to improve, the LPC has again weighed up future risks and, the ability of all employers to pay, in arriving at a recommendation which is above inflation but may not be seen as excessive."
Chris Goulden, head of poverty at the Joseph Rowntree Foundation, said that the level of the national minimum wage "falls well short of the amount people need to cover costs and achieve an adequate standard of living in the UK".
Mr Goulden said the proposed rise would be "a welcome step to easing the strain on households budgets", but added: "We believe bolder action is needed to address low pay and the cost of essentials, such as housing, energy and food.
"Our research shows that the cost of a minimum living standard has increased by a quarter since 2008 - thanks to rising costs and cuts or freezes to tax credits and other in-work benefits. This means the pressure to raise wages has become even greater."
But Mark Littlewood, director general at the free-market Institute of Economic Affairs said: "This increase will have a negative effect on the people it is meant to help: the young and low-skilled. For people out of work, the real minimum wage is zero.
"The national minimum wage has grown faster than average earnings since 2007 and today's recommended 3% increase comes at a time when average wages are still growing slowly. Legislated pay hikes such as this are likely to privilege those in work whilst worsening the job prospects for the most vulnerable."