M'Vila broke down in tears when he was replaced after twisting his right ankle, leaving the stadium on crutches before returning to the bench without them in the second half.
However, France coach Laurent Blanc said he was confident the holding midfielder would be ready to face England in their opening Group D match in Donetsk, Ukraine on June 11.
"In the first half we did a lot of nice things offensively, that was positive," coach Laurent Blanc told French TV channel TF1.
"The players were in better shape than against Iceland (in a 3-2 win on Sunday). We were better physically but we are not ready yet, we suffered in the last 15 minutes."
Blanc was disappointed that M'Vila, who is poised to start at the tournament, only managed to play for a few minutes but was optimistic that he would recover in time for the England match.
"We can think that he will be fit for the first game. His participation in the tournament is not in question," he said.
France doctor Fabrice Bryand said M'Vila had suffered an ankle sprain and would undergo a further examination.
"The ankle is not broken. It's reassuring. We, however, need 48 hours more to say if he will recover in time for the Euro," he said.
