The French forward picked up the problem as he turned to shoot in the 15th minute of the Premier League clash at the Liberty Stadium.
Without a recognised striker on the bench, manager Garry Monk turned to Marvin Emnes to fill the void on the day.
Gomis' absence leaves Nelson Oliveira, on loan from Benfica, as the only out-and-out frontman in the Swansea squad.
The Portugal international has made little impact since arriving in January, though, failing to find the net in eight appearances and making just one start.
Swansea visit bottom club Leicester City in the Premier League on Saturday.
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