Gomis came off in the early stages of last weekend's 1-1 Barclays Premier League home draw with Everton and scans have now revealed the full extent of the damage.
The Frenchman will miss league trips to Leicester and Newcastle and the home game with Stoke but hopes to return for the visit to Arsenal on May 11.
"Scans this week revealed a grade two hamstring strain which will keep the French international sidelined for around three to four weeks," said a statement on the official Swansea website.
Gomis' injury has come at the worst possible time as he was finding his best form in a Swansea shirt after a difficult first season at the Liberty Stadium.
The 29-year-old spent the first half of the campaign in Wilfried Bony's shadow and appeared to be agitating for a move until the Ivorian was sold to Manchester City in January for an initial £25million fee.
But Gomis, who joined from Lyon on a free transfer last summer, has since settled at Swansea and had scored four goals in seven games before being injured against Everton.
Loan signing Nelson Oliveira and Marvin Emnes will compete to fill Gomis' spot at Leicester on Saturday
Source : PA
Source: PA