Carroll scored his first goal in nine months when he headed in Aaron Cresswell's cross after coming on as a substitute in West Ham's 2-1 win over Chelsea on Oct. 24, but has not found the back of the net since.
"We have Andy Carroll situation where he is feeling his groin and he could miss the Swansea game which is a big blow. It's one game," Bilic told reporters on Friday.
"It's nothing major. The scan showed a little bit of a problem. Not long term but it's very unlikely he's going to play."
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Bilic's men are eighth in the table and despite a run of six games without a win, the manager is confident the Hammers can pick up three points by exploiting spaces in Swansea's defence.
"The keys to beating Swansea? I watched their last five games and they didn't play the best. Sometimes they showed good quality going forward but they were open at the back," Bilic said.
"We must be as compact as them and then we have the quality to beat them. We have to show more quality in the final third.
"I'm really confident for Sunday's game against Swansea and if we keep the team spirit when players come back, it's all positive."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
