The club didn't provide a timeline for his return, but the 19-year-old won't play in the NHL this season, The Athletic's Michael Russo reports.
Rossi was ruled out indefinitely with an upper-body injury earlier in January. The ailment stems from having COVID-19 in November, according to Russo.
Minnesota drafted Rossi ninth overall in 2020 after he posted 120 points in 56 games with the OHL's Ottawa 67's last season.
Rossi captained Austria at the 2021 world juniors in Edmonton, going pointless in four contests.