But Bilic will be able to call on striker Andy Carroll, who is expected to return to the starting lineup after a groin injury.
Antonio, the club's top scorer with nine goals, limped off in the first half of West Ham's 1-0 victory over Swansea last weekend. Hamstring problems had also forced him to withdraw from the England squad last month.
"He's one of our best players and of course it is a big blow that we are going to be without him until the end of the season," Bilic told a news conference on Thursday.
West Ham were on a seven-game winless run before the Swansea win, which pushed them up to 14th in the league and eight points clear of the relegation zone.
Bilic is hopeful that gap will increase after Saturday's trip to the Stadium of Light.
Read the full article on eurosport.co.uk: West Ham's Antonio to miss rest of season with hamstring injury