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.
France prevailed in Reims with early goals from Franck Ribery and Florent Malouda as they played eye-catching, free-flowing football in the first half.
Les Bleus dominated the early stages against a Serbia side lacking most of its star players, and Ribery opened the scoring in the 11th minute.
It was the 29-year-old's second goal in as many games after going for three years without netting for his country.
The Bayern Munich star was the instigator of the goal as well as the scorer, as he ran at Toulouse defender Pavle Ninkov then set up Gael Clichy down the left.
The full-back's cross was punched out by Serbia goalkeeper Zeliko Brkic, but straight into the path of Ribery, who had continued his run to slam the loose ball into the net despite the best efforts of Slobodan Rajkovic on the line.
Malouda made it 2-0 five minutes later, with an empathic 35-yard curling effort that fizzed past Brkic.
The goal came from some sloppy play in midfield from Serbia, as Anthony Reveillere robbed Bosco Jankovic with ease 25 yards from goal to set up the Chelsea man for his ninth international goal.
Ribery and Karim Benzema were linking brilliantly in the final third, and they combined in the 40th minute to set up the Real Madrid man for an effort on goal after a one-two on the edge of the box.
Serbia captain Branislav Ivanovic was able to clear after the 24-year-old had failed to get enough of a touch on a backheel, but the loose ball soon found Samir Nasri down the left.
The Manchester City playmaker, so often disappointing in the blue of France, drove low across the six-yard box, but Brkic made a brave point-blank save to deny Malouda.
Serbia had a rare sight of goal two minutes before the break, when Yohan Cabaye conceded a foul 30 yards from goal, but Jankovic's optimistic effort sailed well wide to the right of Hugo Lloris's goal.
The second half was ruined by a spate of substitutions, and it was Serbia who looked the more dangerous in a bitty second 45 minutes.
Three minutes in, the far from impressive Philippe Mexes was penalised for a high boot on Jankovic, and Ivanovic's fierce free-kick from distance was well tipped over by Lloris.
Lloris also made good saves to deny shots from distance from Tadic in the second-half, as the game petered out as a contest.
France coach Blanc will have been delighted by the performance of Alou Diarra, who did not put a foot wrong after coming on for M'Vila, but he will have learned little from a second half that saw five France substitutions and five from Serbia boss Sinisa Mihajlovic.
France’s final friendly game is against Estonia in Le Mans on June 5, six days before their opening Euro 2012 match against England in Donetsk.