Mvila 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.
France, who start their Euro 2012 campaign against England on June 11 in Donetsk, Ukraine, prevailed with early goals by Franck Ribery and Florent Malouda as they played eye-catching, free-flowing football in the first half.
"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 did not comment on Mvila's condition.
France went ahead in the 11th minute when Ribery volleyed home after Zeljko Brkic parried a Gael Clichy effort into the path of the Bayern Munich winger.
Four minutes later, Malouda struck a fierce drive from 30 metres to make it 2-0.
France continued to push hard for more goals but failed to breach the Israel defence again and gradually ran out of steam.
Les Bleus face Estonia in a friendly in Le Mans on Tuesday.