Manager Sam Allardyce confirmed the defender will miss a significant chunk of the Hammers' fight to avoid relegation.
O'Brien landed awkwardly following an off-the-ball push from Chelsea defender Gary Cahill as the players positioned themselves at a corner, leaving the Hammers to defend stoppage time with 10 men.
"The only disappointment for us today was the two injuries," said Allardyce, following the 0-0 draw at Stamford Bridge.
"Joey, unfortunately, has dislocated a shoulder, which is bad news for us.
"That's our third dislocated shoulder this season. I don't think I've had three dislocated shoulders in my entire career, let alone three in one season."
Asked the likely length of absence, Allardyce said: "Ten to 12 weeks."
Mohamed Diame will be assessed ahead of Saturday's home match with Newcastle after suffering a bang on the knee when he fell over the advertising hoardings and had to be replaced in the first half.