But it is unlikely he will be fit enough to be considered for their trip to Valencia in the Champions League on Wednesday and Terry could also miss England's Euro 2008 qualifiers against Estonia and Russia next month.
A spokesman for Chelsea declared: "John is seeing the specialist tonight and will undergo surgery tomorrow morning."
Avram Grant confirmed that Terry wanted to play on and revealed his players believed Dempsey's elbow had caused the damage.
Grant said: "He didn't complain about it at half-time and he wanted to continue but we didn't want to take a risk. For me if it is something with the head, you don't have to take a risk.
"I didn't see the challenge so well. The players mentioned it and said it was an elbow.