Gomis had to be replaced in the early stages of his side’s recent 1-1 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 is hopeful of returning for the trip 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 for the Swans 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.
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 will compete with Marvin Emnes to fill Gomis’ spot at Leicester on Saturday.