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.
"Sunderland is in a situation that they are desperate for a win," the 48-year-old Croatian added.
"We know it's going to be extremely hard, but it's a good opportunity for us to get some points and get closer to safety."
Bilic said Carroll, formerly with Sunderland's North East rivals Newcastle United, would be fit enough to share the striker's role with Jonathan Calleri.
"Andy could (have played) ... for 15-20 minutes against Swansea, but this Saturday is completely different... We're likely going to need both Andy and Jonathan ...and they'll share the minutes on the pitch," the manager said.
Hammers' skipper Mark Noble is suspended, having picked up his 10th yellow card of the season against Swansea.
(Reporting by Hardik Vyas in Bengaluru; editing by John Stonestreet)
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