The Jets said before their game Tuesday at Minnesota that Wheeler was symptomatic after testing positive for the virus.
According to NHL rules for this season, that means Wheeler must isolate from the team for at least 10 days and will need a doctor's approval to return once symptoms are gone. On Monday, Wheeler was placed in the league's COVID-19 protocols.
The Jets host Anaheim on Thursday and Nashville on Saturday before playing at Anaheim on Oct. 26, all games that 35-year-old Wheeler will be absent for in addition to the matchup against the Wild in the area where he grew up.
"We focus on today, the guys that are playing," coach Paul Maurice said after the team's morning skate. "Then we'll make sure he gets lots of phone calls as soon as he's feeling 100%."
Wheeler had one assist in Winnipeg's first two games this season. The 14-year NHL veteran had 15 goals and 31 assists in 50 games for the Jets last season.
No other positive tests were reported by the Jets. All of their players are vaccinated.
"Obviously the virus is still around and you've still got to be aware of it, so just extra precaution," said center Mark Scheifele.
Andrew Copp was expected to slide into Wheeler's spot on the top line.
"I don't know if scary is the right word, but it kind of gives us a jolt that it's still around," Copp said.
The Jets, back in the Central Division with traditional realignment returning this season, entered Tuesday in last place, at 0-2, four points behind the Blues and Wild.
The Associated Press contributed to this report.