The Cardinals also said Watt, 33, will not be present for the team's trip to Tennessee this week.
The Cardinals are set to travel to Tennessee on Tuesday to practice against the Titans on Wednesday and Thursday. They'll play the Titans in the third preseason game Saturday.
Watt will have to isolate for five days, according to the NFL's most recent COVID protocols.
Watt missed the last 10 games of the 2021 regular season with a torn labrum, bicep, rotator cuff and a separated shoulder. He returned for Arizona's wild-card playoff game, a 34-11 loss to the Los Angeles Rams.
Watt is the second high-profile Cardinal to miss time this camp because of COVID. Quarterback Kyler Murray missed five days and was slow to return to action after testing positive earlier this month.