The France international, who is on loan from Newcastle, suffered the problem during his country???s 1-1 draw with Albania on Friday.
A statement from Roma read: “Yanga-Mbiwa underwent medical tests today that confirmed a grade-one strain to his right thigh.??The player has already started treatment for the injury.”
Yanga-Mbiwa will miss the Serie A matches against Atalanta, Inter Milan and Sassuolo, and next week’s Champions League encounter at CSKA Moscow.
But the 25-year-old could return for Roma’s Champions League clash against Manchester City on 10 December at the Stadio Olimpico.
Yanga-Mbiwa’s absence is a blow for Roma coach Rudi Garcia, with the player having started in eight league matches for the team this season.
Roma head into Saturday’s match at Atalanta in second place in the league, three points adrift of league leaders Juventus.