Bayern team-mate Ribery admits his absence is a big loss to Pep Guardiola's side and is desperate for Alaba to reach full fitness as soon as possible.
The also-injured Frenchman told Goal: "It is difficult for him, for his family, for the team and for the whole club. He is so important for us.
"He was already injured before the winter break, but he fought back. He was in peak condition and his performances were great. We have lost a big player.
"Now he has to stay calm and remain optimistic. David is strong enough to deal with it. For us, though, this is a catastrophe. He must return as soon as possible, he's that important to us."
Alaba spent more than two months on the sidelines earlier this season after partially tearing the medial ligament and damaging the meniscus in his right knee during Bayern's 2-0 win over Roma in the group stage of the Champions League.
He joins Ribery (ankle), Javi Martínez (cruciate ligaments), Arjen Robben (stomach) and Thiago Alcantara (knee) on the sidelines, with the Bavarians set to face Borussia Dortmund in the Bundesliga on Saturday.