The 19-year-old, who played six senior games for the Hawks this season, was treated in Darwin for what the club described last week as a "quite severe" bout of pneumonia.
Hawthorn football manager Chris Fagan said Anderson would not attend the club's upcoming training camp in South Africa, as he starts on the road back to full health.
"He'll recover and gradually build back up," Fagan said on Monday.
"There's no point in stressing his body by flying to South Africa."
The Hawks' senior players started pre-season training at Box Hill City Oval on Monday morning, nine weeks after winning the 2013 Grand Final.
They will depart for the 12-day training and conditioning camp on Sunday.
Twitter: @AFL_MarkM
