The £71million forward was substituted at half-time of Saturday’s 3-2 defeat to West Ham after hurting his ankle.
There is no prognosis yet about the extent of the injury, but Tuchel confirmed he could not play on, while Marcos Alonso was substituted with a back problem.
He said: “Kai has huge pain, Marcos Alonso has back pain, so that is another two substitutes due to injury. We have to deal with it.”
While Havertz and Alonso have joined a growing injury list for Chelsea, Tuchel admitted he cannot put a timeline on N’Golo Kante’s return from a twisted knee, adding that Jorginho is playing through the pain barrier at the moment.
“I actually have no idea when he will be back and we are missing not only N’Golo, also Mateo Kovacic since five or six weeks ago,” said the Chelsea manager. “Jorgi is playing with hip pain for many matchdays and you can see it. That is the situation.
“It is not interesting what I think (about Kante’s return). He plays when he is back. He has a long way to go, if I say now he plays at Zenit [on Wednesday] and he doesn’t play, then that doesn’t help.
“I take care of the injured players. N’Golo has not been on the pitch since Juventus.”