Vlastuin, who has played every game this season, suffered the injury in Richmond's 17-point loss to Melbourne last Saturday.
The best-case scenario for the valuable 20-year-old, who has been earmarked as one of the Tigers' future midfield stars, is to return against Fremantle at the MCG in round 13.
Tall forward Liam McBean also faces a month on the sidelines after breaking his finger playing for the Tigers' VFL team on Saturday.
Captain Trent Cotchin is recovering from an ankle injury and will need to pass a fitness test to face Greater Western Sydney at Spotless Stadium this week.
The star midfielder has said he is confident he will be available after playing through the injury against the Demons.
Defender David Astbury will undergo surgery to repair a dislocated kneecap, with his recovery timeline yet to be determined.
His injury opens the door for the Tigers to upgrade in-form midfielder Anthony Miles from the rookie list, with the former Giant pushing to play his first game for his new club against GWS this week.