"We have one player injured and that's Adrian," manager Slaven Bilic told reporters on Friday.
"He will ... probably miss the last two games as well. We've got a great deputy, he was one of the biggest reasons we went quite far in the FA Cup," added Bilic, referring to the London team's run to the quarter-finals.
Sixth-placed West Ham trail Manchester City, who are fourth in the Premier League and hold the final Champions League qualifying spot, by five points.
Bilic's men have three games remaining while City have two matches left.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
West Ham are unbeaten at home in the league since August and Bilic said they were fully concentrated on Swansea, not on an emotion-filled final game at the Boleyn Ground against Manchester United on Tuesday.
"We need to be totally focused on Swansea, not thinking about Man Utd," he added.
Co-owners David Sullivan and David Gold have urged West Ham fans not to invade the playing surface after the game against United.
"Any incursions on to the pitch will certainly mean cancelling the squad's richly deserved lap of appreciation and denying some of our greatest ever players the chance to take the field for the final time," Sullivan and Gold said in a joint statement.
"That would be a tragedy for them and the Boleyn Ground," the pair added of the club's home for the past 112 years.
(Reporting by Shravanth Vijayakumar and Nivedita Shankar in Bengaluru; Editing by Tony Jimenez)
