Arians has been sick for the majority for the week, according to the Colts.
The illness was first reported by the Indianapolis Star.
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.
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