Tomkins is reported to have sustained the injury during training on Thursday, with the club confirming he later received treatment at hospital.
No timeframe has been put on a return for Tomkins, but he could be ruled out for the rest of the season.
The news is a further blow to manager Sam Allardyce, who is already without fellow centre-back Winston Reid for Saturday's Premier League trip to Arsenal.
"West Ham United can confirm that James Tomkins has suffered a dislocated shoulder," the club posted on their official Twitter account.
"The 25-year-old was taken for hospital treatment and will continue to be assessed by the club's medical staff."
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