The 26-year-old had to be replaced by Matt Taylor just after the hour-mark after falling awkwardly following a challenge with Arsenal goalkeeper Vito Mannone.
"It looks like a dislocated shoulder and that's anything from eight to 12 weeks out," manager Sam Allardyce told the club's website.
"We can't get it [put] back [in] so he is going to have to go to hospital to have an anaesthetic put in it to slot the shoulder back into the socket," he said after the match.
"The specialist will determine how long it will take to sort that out so it is a bit of a shame, but we all suffer injuries and we just have to make sure we use the squad we have got."
West Ham's Ivory Coast defender Guy Demel and New Zealand international Winston Reid were also injured in the London derby.
"I think Guy Demel has pulled a thigh muscle and that could be four weeks out and Winston Reid had a back spasm and we couldn't bring him off because we'd used all of our substitutes," said Allardyce.
Arsenal's win took them up to fifth in the table, seven points behind leaders Chelsea. West Ham are eighth.