Portuguese striker Vaz Te had to go off during the first half of the goalless draw at the Liberty Stadium and faces a spell on the sidelines.
The Hammers have told Press Association Sport there is no timescale for his recovery at the moment.
However, there will be concern at Upton Park as the 27-year-old suffered a similar injury last season which required surgery and kept him out for almost three months.
Boss Sam Allardyce is already without his main striker Andy Carroll, who has yet to play this season due to a foot injury.
Carlton Cole, who came on as a second-half substitute at Swansea, is in line to make his first start since re-signing for the Hammers when they travel to Burnley in the Capital One Cup on Tuesday night.
Source: PA
Source: PA