The 22-year-old was involved in a full-contact drill and injured his right AC joint while tackling.
North Melbourne Senior Performance Consultant Steve Saunders said Anderson will miss the opening rounds of the season.
“He had a reconstruction of his left shoulder before coming to North, and has injured the right AC joint. We expect him to resume full training in four to six weeks,” Saunders said.
“We expect him to be fit and available within the first few weeks of the season.”
Anderson joined the Roos from Hawthorn via trade in 2015 and has made 10 appearances for the club since the switch.