The 26-year-old withdrew from England duty last month with a hamstring injury, but recovered in time to face Arsenal in midweek.
He was brought off against the Gunners with illness and again failed to complete 90 minutes as he suffered a hamstring injury against the Swans on Saturday.
Antonio limped from the field with his head in his shirt as Jonathan Calleri was thrown on in his place.
And the Hammers were dealt a further blow as Mark Noble - marking his 400th West Ham appearance - picked up his 10th yellow card of the season for a rash challenge, ruling him out of West Ham's next matches against Sunderland and Everton.
West Ham had lost five games in succession going into Saturday's game, but took the lead in the first period courtesy of Cheikhou Kouyate.
It comes after Slaven Bilic received a public vote of confidence from the club's board last week, while Standard Sport understands the Croat will remain in charge until the summer regardless of results.