Vaz Te had to be replaced by Matt Taylor just after the hour-mark after falling awkwardly following a challenge with Arsenal goalkeeper Vito Mannone.
Hammers boss Sam Allardyce confirmed after the match that the 26-year-old would not be fit to return until after the international break and could be out until the festive period.
"No he won't be right, it will be six to 12 weeks depending," he said.
"We can't get it back 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.
"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."
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.