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.
Hammers boss Sam Allardyce confirmed after the match that Vaz Te 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."