The Brazilian stopper was forced off against the Giallorossi during the first half and will now be ruled out of his side's crucial European tie with the Blaugrana on Wednesday
The defender was a doubt for the fixture against the Giallorossi and was expected to be rested for the game after picking up a knock during last week's 2-2 draw with Juventus in the Coppa Italia; a result which saw Massimiliano Allegri's men crash out 4-3 on aggregate.
However, the former Fluminense defender was put through his own personal warm-up prior to kick-off and deemed fit enough to start versus Roma, only to be hauled off after just 10 minutes with a troublesome flexor muscle.
"Thiago Silva has a problem with a flexor muscle and cannot play in the Champions League against Barcelona. I risked him, but it did not pay off," Allegri told Sky Sport Italia after the match.
Silva's injury could prove to be a big blow for the reigning Italian champions, who are already set to be without a host of players for Wednesday's first-leg encounter against Barca.
Nevertheless, the win against Roma means Milan move seven points clear of Juventus at the summit of Serie A, thanks to a pair of goals from Zlatan Ibrahimovic.