The 27-year-old suffered a dislocated shoulder in Sunday's goalless draw at Swansea and faces a lengthy spell on the sidelines.
It is not yet known how long he will be out of action for but the former Portugal Under-23 star missed three months of last season after suffering a similar injury.
The injury is a further blow for boss Sam Allardyce, who has had to cope without England hit-man Andy Carroll this term.
The former Newcastle man is currently undergoing intense physiotherapy to try and regain fitness from a foot injury but is still a few weeks away from a return.
In his absence the Hammers have managed to take nine points from nine games and currently sit in 15th place in the Premier League table.
Punters looking to use a free bet might fancy the Upton Park club to struggle with relegation this season with so many injury problems and they are next in top-flight action at home to Aston Villa on Saturday, November 2.
The East End club will be in Capital One Cup action before that clash, however, and face Championship high-flyers Burnley on Tuesday evening at Turf Moor.