Defender Reid was injured in training on Wednesday and could be set for a long spell out, with the results of a scan expected on Friday.
On-loan Chelsea winger Moses picked up his injury against Manchester United last weekend and manager Slaven Bilic has ruled him out for four to six weeks.
They are the latest additions to a growing casualty list at Upton Park which threatens to derail their fine start to the season.
The Hammers have already lost Dimitri Payet and Diafra Sakho until February while Manuel Lanzini is out for six weeks with a thigh problem suffered in training.
Enner Valencia has been out for five weeks with an ankle injury but he could give Bilic a boost by being added to the squad to face Stoke on Saturday.
Bilic said: "Reid got injured in training, it doesn't look good
It's one of those they tell you is four to six weeks but it doesn't look like a small one
He slipped and felt it rupture.
"Victor is out for four to six weeks
It's a blow, we have had six injuries since the Everton game
Before that we had a full squad, then Payet and Valencia were injured against Everton and now we have four muscle injuries."
Source : PA
Source: PA