The 29-year-old went under the knife to repair ligaments in his right wrist.
A club spokesperson said Gibson would initially be unable to participate in contact drills when the Hawks returned from their off-season break, but would still be able to run.
He will resume full training in the New Year.
Hawthorn also announced on Thursday that rookie-listed players Andrew Boseley and Amos Frank had been delisted after two years at the club.
They join Lance Franklin, who has defected to the Sydney Swans, and Brent Guerra, who has retired, in departing the Hawks since the end of the season.
Frank was a speculative pick-up from the remote Anangu Pitjantjatjara Yankunytjatjara (APY) Lands in far-north South Australia, and did not speak English when he arrived at Waverley.
He showed some good form in 2012 with Hawthorn's VFL affiliate Box Hill but, hampered by injury, was not able to continue his progress this season.