Gray, who has 77 caps for Scotland, suffered the injury during Exeter's 47-28 Champions Cup semi-final defeat to La Rochelle in Bordeaux.
"From what I've been told unless the operation goes exceptionally well and his recovery is exceptionally quick, I would say he is very doubtful for the World Cup," Baxter told a press conference on Wednesday.
"It's a patella tendon injury, he's dislocated his kneecap. Fortunately, the other major ligaments within the knee are all stable.
"It's a relatively complex patella tendon injury, which is going to require surgery this week, and there's a relatively long period of rehab," Baxter said.
The World Cup will be held in France from September 8th-October 28th. Scotland are in Pool B and begin their campaign against defending champions South Africa.
