Brate underwent arthroscopic surgery last week to repair the injury, which included the removal of bone fragments. He is currently on crutches. Recovery time will be a "few months," the source said.
The expectation is that the Bucs will ease Brate back into action during OTAs with the hope of participation in the June minicamp.
Before his firing, former Bucs head coach Dirk Koetter indicated Brate had been fighting through an injury.
"Cam's been playing hurt this whole year," Koetter said. "He hasn't been healthy from day one. He's done an unbelievable job of fighting through it. He's another guy that if you knew the amount of rehab Cam does on a weekly basis just to be able to play, it's pretty remarkable that he's out there playing at all."
The hip labrum is a band of cartilage that surrounds the outside rim of the hip socket and works to add cushion and stabilize the joint. Playing through an injury to it can be very painful.
Brate caught 30 passes for 289 receiving yards in 2018. While his yardage and catches may have been down from the past two years -- partly because of the emergence of O.J. Howard -- Brate remained one of the Bucs' top scoring weapons.
His six touchdown catches were tied for fourth-most in the NFL among tight ends. Brate's 20 touchdowns since 2016 are tied with Zach Ertz for second-most in the NFL.