Del Rio went 68-71 from 2003-11 as head coach of the Jacksonville Jaguars before joining Fox's staff last season.
Del Rio will continue to serve as Denver's defensive coordinator.
The Broncos are ranked 24th in the NFL in defense this season, but they were missing star linebacker Von Miller and cornerback Champ Bailey for much of the first half of the season.
Fox needs aortic valve replacement surgery and will miss several weeks. He was taken to a hospital near his Charlotte, N.C., home Saturday when he began feeling dizzy while playing golf during the Broncos' bye week.
The Broncos (7-1) play at San Diego on Sunday
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