The Portuguese forward dislocated his shoulder in the second half of the Hammers' Premier League loss to Arsenal this evening.
Speaking after the game, Allardyce confirmed the extent of the 26-year-old's injury: "No, he won't be right, it will be six to 12 weeks depending.
"We can't get it back so he is going to have to go to hospital to have an anaesthetic put in it to slot the shoulder back into the socket.
"The specialist will determine how long it will take to sort that out so it is a bit of a shame, but we all suffer injuries and we just have to make sure we use the squad we have got."
Defeat for West Ham leaves them eighth in the table.