Hamlin-Uele finished his first stint during the Sharks' 52 points to 16 win over the St George Illawarra Dragons on Thursday night, but didn't return during the second half.
Fitzgibbon said the injury was likely to be rib cartilage, and was "bizarre" given the prop finished his first stint playing after suffering the injury.
The coach also said he believed a shoulder charge had caused the injury.
“I'm not sure. It was off the kick-off and looked like a shoulder charge to me, I'm not sure there,” Fitzgibbon said on Hamlin-Uele's injury.
“Not sure if it's rib cartilage, a broken rib or something like that, but he finished that stint so it was kind of weird. It finished okay and he knew he had something, and it got worse at halftime, so we couldn't get him back up after halftime.
“It's going to be cartilage or something like that, but it's bizarre he finished a pretty good stint there so hopefully that's a good sign."
Hamlin-Uele will go for scans to confirm the injury is not a fracture or break in the ribs, with it being the props third injury in 12 months after he left the Rugby League World Cup early, and then suffered an ankle injury during Round 9 against the North Queensland Cowboys.
Coach Fitzgibbon said that while injuries had been frustrating in the middle third, all players called upon at the club had been standing up to get the job done.
“We have been turning them over a little bit, but they have been performing pretty strongly - everyone is sharing the workload there,” Fitzgibbon said on injuries in the middle.
“Tommy [Tom Hazleton] was strong again tonight and I think Dale [Finucane] has had his best two games for the club in the last two weeks.”