The Flames receive a 2016 second-round and a 2018 fourth-round pick in the deal.
The Panthers currently sit atop the Atlantic Division standings with a three-point lead over the Tampa Bay Lightning with one game in hand. The Flames, one of the biggest surprises of the 2014-15 season, are in sixth place in the Pacific Division.
Hudler, 32, is in the final year of a four-year, $16-million contract.
Hudler has 10 goals and 35 points in 53 games this season to go along with a minus-1 rating.