The Spaniard, a summer signing from Swansea, suffered the injury during Saturday's 3-0 defeat at Crystal Palace.
Manager Gus Poyet told The Argus: "He has got a broken rib and he is going to be out for a while. It is going to be four to six weeks, depending on the healing process for Andrea.
"He didn't play a lot at Swansea, so we have tried to keep an eye on him because of the football he has missed in the past.
"Everything we have done until now is going to be gone. In a month-and-a-half we will have to start from zero with him, so it is very unfortunate and then, of course, there's his quality as well.
"He has been getting more influential in the team and also with set plays, so it's a blow but that is why the squad is there, to make sure we don't miss him too much."
Poyet also has injury concerns over Wayne Bridge and Adam El-Abd ahead of Saturday's trip to Charlton, while Marcos Painter is definitely ruled out and Lewis Dunk is suspended.