Nolan damaged his shoulder in training on Thursday, missing the Hammers' 3-1 Premier League victory at Crystal Palace on Saturday.
Sam Allardyce: "Kevin fractured his shoulder and that's a massive blow to us, along with all the other players we've got injured.
"He will be out for probably six weeks I would think.
"It isn't a dislocated shoulder, it's a fractured shoulder, but I don't know just how long that will keep Kevin out.
"We dealt with it brilliantly at Palace and let's hope we can continue to do that.
"It didn't affect us at Palace and maybe that's a sign there's more to come."