Bergessio sustained the injury after a strong tackle from defender Giorgio Chiellini in Wednesday's 4-0 loss at Juventus, but remarkably completed the match.
A statement from the club read: "Having been challenged by Juventus defender Giorgio Chiellini, Bergessio sustained last night a fractured fibula in his left leg.
"We wish our number nine, who stayed on the pitch until the end of the game despite his injury, a speedy recovery."
Catania president Antonino Pulvirenti accused Chiellini of using excessive force.
"It was a challenge of unprecedented violence, a presumptuous and cowardly act," he said to Gazzetta dello Sport.
Chiellini Tweeted: "I wish to publicly apologise to Bergessio for the foul that caused his injury.
"I went for the ball but he anticipated me and unfortunately I hit his leg.
"I am truly sorry and wish him the best of luck for a prompt recovery."
Catania have suffered a blow with news that Argentinian striker Gonzalo Bergessio will be sidelined for at least two months with a fractured fibula in his left leg.The 29-year-old Bergessio has scored one goal in nine league appearances for Catania this season.