Arians has been sick for the majority for the week, according to the Colts.
The illness was first reported by the Indianapolis Star.
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He'll be replaced by quarterbacks coach Clyde Christensen, a former Colts offensive coordinator.
Arians was the interim coach for the Colts since October after coach Chuck Pagano was diagnosed with a rare form of leukemia, which he has bravely battled to return to the sidelines for the AFC South team's regular-season finale win over the Houston Texans last week.
The Colts are 11-5 for the season, going 9-3 under Arians' leadership.
Arians has been linked to the Chicago Bears' head coaching vacancy.