Njoku, who exited Monday's win against the New York Jets with a concussion, is getting additional medical opinions to find out if surgery is necessary and how long he might be sidelined.
Both the wrist injury and the concussion occurred on the same play, when Njoku was upended by Jets cornerback Nate Hairston on a passing attempt from quarterback Baker Mayfield in the first quarter.
"David is a good player, so definitely him being limited right now or whatever presents problems for us," Cleveland coach Freddie Kitchens said Wednesday. "This game in the National Football League is about attrition, so you have to deal with it on your side, and other teams do as well. We will get the next guy in there and make sure he knows what to do. When somebody goes down, that is another opportunity for someone else, so we will see how it goes."
If Njoku is sidelined, Demetrius Harris likely will become Cleveland's starting tight end. The Browns acquired Harris from the Kansas City Chiefs during the offseason. He has only one catch for 4 yards this season, and no other Cleveland tight end has a target through two games.
Njoku has seven receptions and a touchdown this season. He was Cleveland's second-leading receiver last year, with 56 receptions for 639 yards.
The Browns play host to the Los Angeles Rams on Sunday night.