Outside centre Suaalii suffered the injury during the Waratahs' warmup ahead of Friday's Super Rugby match against the Hurricanes in Sydney, which the home side went on to lose 59-19.
The 22-year-old won't return to play until the second half of the season, in a major blow to their chances.
"Following results of a scan yesterday, the centre will now miss six to eight weeks of action," a Waratahs statement said.
Coach Dan McKellar said after his team's first defeat of the season that Suaalii is a "top quality player", whose absence was keenly felt.
The former rugby league star switched codes in a high-profile move in late 2024 and has played 18 Tests for the Wallabies.
He only played seven games for the Waratahs in his maiden campaign last year because of injuries as they missed the play-offs for a second straight season.