The North Melbourne captain returned home on Monday after he went under the knife on Sunday morning.
The club's director of medical services, Steve Saunders, said the 26-year-old would be measured on a weekly basis in his recovery but should be running by Christmas.
"There will be a number of weekly measurements that we'll take to see how he's tracking, and nothing is ever set in stone, especially with these types of repairs," Saunders told the club's website.
"But all indications are that by December, Andrew should be able to start some running on the Alter-G treadmill, with very low percentages of body weight."
Swallow suffered the injury in his side's thumping win over Melbourne on Saturday.
He will be in a plaster cast for two weeks and will then move into a moon boot to protect the injury throughout his rehabilitation.
"The surgery went really smoothly, the surgeon was really happy with the end result and now Andrew has to rest at home for the next week or so before we get him into rehab," Saunders said.
"He'll be pretty mobile quickly but there's obviously a very careful and gradual loading program that needs to be done over many months.
"The short-term plan initially is just to let the repair heal and let nature do its thing."
While Swallow's injury is likely to see him on the sidelines until the backend of 2014, midfielder Jack Ziebell will be fit to take on Geelong on Friday night.
Ziebell appeared sore during the Demons clash.
"Jack's copped a couple of contusions (corkies) again but he's good," Saunders said.
Callum Twomey is a reporter for the AFL website. Follow him on Twitter at @AFL_CalTwomey.
