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Both parties plan to raise the NMW significantly if they are elected.
The IFS said at some point higher wages would hit employment, penalising workers who are supposed to benefit from higher pay.
Labour said its plan would increase living standards, while the Tories declined to comment.
A Labour spokesperson said: "Labour's £10/hour minimum wage is in line with reputable forecasts of the wage needed to maintain a decent standard of living by 2020 and put an end to poverty pay."
Some Conservative MPs have said higher pay for workers is also good for businesses.
In its report, the IFS said increased wages for lower-paid workers has to be paid for by reduced profits, higher prices or lower earnings for the better-off.
"Crucially, there must also be a point beyond which higher minimum wages have substantial impacts on employment," it said.
There may be a case for gradual increases in the minimum wage, it argued, "but increases on the scale, and at the speed being proposed, create big risks".
Although the Conservative manifesto has not yet been published, the party's existing plan is to increase the National Living Wage - for those over 25 - from £7.50 to as much as £9 an hour by 2020.
When he was chancellor, George Osborne said the level should reach £9 an hour by 2020. However the Office for Budget Responsibility has estimated the figure will be £8.75, as the increase is linked to average earnings.
Labour plans to increase the NMW to £10 an hour by 2020. It also wants to extend that rate to all those between the ages of 18 and 25, except for those on the apprentice rate.
Currently those between 18 and 20 years old earn a minimum of £5.60 an hour, while those between 21 and 24 earn a minimum of £7.05.
The IFS calculates that both Labour and Conservatives are planning for a "dramatic" increase in the number of workers affected by the minimum wage.
Just 8% of those over 25 are paid the National Living Wage.
Under the Conservatives, this would rise to 12% by 2020. Under Labour, it would be 22%.
That is roughly comparable with what happens in France, which has the highest such level among OECD countries.
The IFS says both Labour and the Conservatives are moving away from the current arrangements, under which the Low Pay Commission recommends an appropriate level for the NMW.
When making its recommendation, it considers the effect on jobs.