The midfielder was substituted for Cody Gakpo in the 61st minute and will now undergo further assessment to determine the severity of the problem.
However, Klopp is hopeful that the injury is nothing more than a minor setback.
The Liverpool boss said: “We will see. They told me directly after the game it got worse during the game, so that means it was not 'bam'. He felt a little bit and didn’t show immediately.
“We hoped it would go by, [but] it didn't. There was this really intense sprint with the ball which ended on the 18-yard line with a collision.
“I hope it is not that serious but we have in the next 10 days three more games, so I don’t know if he will be part of them or one of them. We will see, we have to make a scan.”
Gravenberch has enjoyed a prosperous start to life on Merseyside since his deadline day arrival at the end of the summer transfer window.
Bagging two goals and two assists, he has looked a live wire in his early days as a Liverpool player, and was one of the few bright sparks in an underwhelming first half between the Reds and Manchester United.
With Alexis Mac Allister having recently joined long-term absentees Stefan Bajcetic and Thiago on the sidelines, Klopp will be eager not to lose another midfielder to the treatment table.