Gudbranson, the third pick in the 2010 NHL Draft, has been sidelined with a shoulder injury which occurred during the summer while wakeboarding, and the Panthers sent him to the San Antonio Rampage on Wednesday.
Gudbranson is scheduled to make his AHL debut Friday night when San Antonio plays host to the Rockford IceHogs.
After spending the 2010-11 season in the Ontario Hockey League, Gudbranson went straight to the NHL, where he played in 72 games for the Panthers last season.
Florida coach Kevin Dineen said there was no set number of games he wanted Gudbranson to play in the AHL.
"It depends on what we think of him," Dineen said. "We'll see where he's at. We'll watch the game tomorrow night and see how he's doing and go from there. He's got to go down and establish his play, and play."
Gudbranson was one of two Panthers players loaned to San Antonio, the other being forward Mike Santorelli.
After clearing waivers before the start of the regular season, Santorelli opened the season playing on the first line but was dropped to the third line after the game and was a healthy scratch three of the past four contests.
Santorelli didn't have a point in three games this season. He had 20 goals in 82 games in 2010-11, but had nine goals and two assists in 60 games last season.
"I've always been a believer that Santo is a top-six player," Dineen said. "That's his skill set, as a higher-end skilled forward. Unfortunately, we don't have that fit for him right now. He's got to either diversify his game or get a major dose of confidence. I feel that some time in the American League is going to give him that jolt and that quality ice time that he'll need to get things turned around.
"That book is not closed yet, but he's got to go down there and expand his game and as much so get his confidence back."