The England striker went down under pressure from Chelsea defender Cesar Azpilicueta but was unable to continue and was replaced by Jay Rodriguez.
It is the latest in a long line of injury problems for Sturridge, who was making his second start for West Brom since joining on loan from Liverpool for the rest of the season.
The 28-year-old struggled for opportunities under Reds boss Jurgen Klopp, starting 20 of a possible 94 Premier League games under the German.