And the club captain will miss Saturday's trip to Fiorentina as well as the Group G game away to CSKA four days later, and possibly more matches beyond.
"De Rossi won't be involved against Fiorentina or CSKA - and he may miss the Sampdoria game too," Di Francesco told a news conference.
That injury could prompt Di Francesco to change up formations, but admitted that how they played after De Rossi's injury did not fill him with much confidence.
“That's a possibility although I didn't like the way we played with three in midfield against Napoli – we were too submissive," the Roma boss said. "It's one of the things I have to weigh up. I haven't decided yet but I think I'll stick with the system we've been using recently.
"I prefer not to change the shape of the team too much at the moment.”
Di Francesco also addressed whether Bryan Cristante, who replaced De Rossi against Napoli, would keep that place for the match against Fiorentina, dismissing questions over the midfielder's fitness, but saying the coaching staff is still working on the mental aspects of his game.
“I read somewhere that Cristante is supposedly not on the same physical level as other players but the fitness tests we did this week showed he's actually one of the fittest," Di Francesco added. "The mental side of the game is fundamental for all players. We're working with him, he's training well and is very willing to learn.
"I don't know if he will replace De Rossi. [Lorenzo] Pellegrini can play in that central midfield role too, as he has on other occasions.”
Roma, who reached the semi-finals of the Champions League last season, are level on points with Real Madrid after two wins from three Group G matches.
Di Francesco's side are struggling in Serie A, however, sitting eighth in the table after failing to win either of their most recent two games.