Allardyce said club captain Nolan suffered the injury during training on Thursday and was forced to miss the Hammers' 3-1 Premier League win at Crystal Palace on Saturday.
The West Ham boss admitted Nolan's influence will be missed, but backed "the best and strongest squad I've put together at the club" to handle his absence.
"Kevin fractured his shoulder and that's a massive blow to us, along with all the other players we've got injured," said Allardyce.
"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."
Allardyce believes the comfortable victory over Palace indicates his squad has decent strength in depth.
The Hammers boss added: "We were missing five players who play a big part in our squad, so to win the game comfortably with as many injuries as that was extremely pleasing.
"So perhaps this might be the best and strongest squad I've put together at the club - I hope it is."