|The animal can be seen twisting and slamming into the water in the boat's wake|
Florida Fish and Wildlife Conservation Commission spokesman Rob Klepper said the men had been identified but their names would not be released until enquiries had been completed.
In the video, the shark is seen twisting in the air and slamming against the water as it visibly struggles in the boat's wake.
One of the men says the shark looks "almost dead", while laughter can be heard in the background.
Three of the occupants of the small boat are visible, but the person filming is not.
It is not clear when or where the footage was recorded, nor whether the men have broken any laws or if the shark was alive at the time, but Mr Klepper said officials found it "disheartening and disturbing".
The video was sent to a Miami sport fisherman, Mark Quartiano, who goes by the nickname "Mark the Shark" - by, he said, two of those involved.
Mr Quartiano said he decided to publish the footage so the fishermen could be identified.
He told CNN he was "horrified" by the video.
"I've been shark fishing for 50 years and I've never seen a disrespect for an animal my entire career that was that evil," he said.
The video has been viewed more than 285,000 on Mr Quartiano's business Facebook page, attracting more than 1,800 comments, many expressing disgust and outrage.
"They thought it was funny, they thought it was cool," Mr Quartiano said. "Even if the shark was dead, you don't do that. It's totally disrespectful."
Florida news station WESH2 said it had obtained a related photo showing what appears to be the same shark ripped to pieces and being held by two men, which it did not publish because it was too graphic.