The centre-back suffered the blow during the DFB-Pokal quarter-final tie against Bayer Leverkusen on Wednesday, which the Bavarian giants won on penalties.
He is joined on the sidelines by Arjen Robben (stomach), David Alaba (knee) and Bastian Schweinsteiger, who has not recovered from an ankle injury and is a doubt for next week's UEFA Champions League clash with Porto.
Franck Ribery is back in training following an ankle problem but could miss the quarter-final first leg with Porto next Wednesday, while Javi Martinez is still out with a knee injury.
"Medhi Benatia is out for two to four weeks," Guardiola said ahead of Saturday's Bundesliga meeting with Eintracht Frankfurt. "Our situation is very critical.
"[Schweinsteiger] will not be there against Frankfurt. I do not know whether [Ribery] can fly with us to Porto on Monday. We must not forget he has missed five weeks."
Asked about a potential return date for Robben, Guardiola added: "Maybe he's back in the DFB-Pokal [semi-final on April 28] against Dortmund. We wait for him.
"We must concentrate on the players that we have. We want to keep on fighting for three titles even in this situation."
