Rivera was placed on the disabled list Sunday because of inflammation in the joint. He had surgery Friday.
Jose Briceno, a rookie who has yet to make his big-league debut, is currently the Angels' backup. Juan Graterol appeared in one game this season while Maldonado was on the bereavement list.
With the extended loss of Rivera, the Angels could be in a position now to pursue a more experience backup.
"Albert's held up very well," Scioscia said. "It's certainly a point that we're paying a lot of attention to. He's bouncing back well. Albert's in great shape.