The 58-year-old Fox will undergo aortic valve replacement surgery early next week at a hospital in Charlotte, N.C.
The Broncos did not immediately name an interim head coach.
Fox had been told earlier about his heart condition and was hoping to put off the operation until February. As part of his trip to North Carolina over the Broncos' bye week, he met with his cardiologist and was told to seek medical attention immediately if he felt any discomfort.
On Saturday, Fox became dizzy playing golf near his off-season home and was taken to a hospital, where tests revealed he couldn't wait any longer to have the surgery.
"I sincerely appreciate all of the support from friends, Denver Broncos fans and so many around the league today," Fox said in a statement released by the team Saturday night. "Although I am disappointed I must take some time away from the team to attend to this pre-existing health condition, I understand that it's the right thing to do. I have great confidence in our coaches and players, who are fully committed to our goals.
"I look forward to returning to coaching as soon as possible."
At 7-1, the Broncos trail the Kansas City Chiefs (8-0) in their division, but they're widely considered Super Bowl favourites in the AFC with a high-octane offence led by Peyton Manning and a star-studded defence that recently was bolstered by the return of All-Pro linebacker Von Miller from a suspension.
Their next game is Nov. 10 against AFC West foe San Diego.
Although it hasn't been determined who will serve as interim head coach during Fox's absence, defensive co-ordinator Jack Del Rio is a logical choice because he spent nine seasons as the Jacksonville Jaguars' head coach before joining Fox's staff last season.
Smyth said Fox was with a group of friends and family on a golf course near his off-season home when he started getting dizzy. He said Fox was "in good spirits and he told me he did not suffer a heart attack."
Running back C.J. Anderson was among the players who sent their well wishes on Twitter, saying, "Prayers go out 2 Fox we here coach."
Fox is in his third season as Broncos coach after a nine-year stint with the Carolina Panthers. He's 107-88 overall, including 6-5 in the playoffs. In Denver, he's 29-14, including 20-5 since quarterback Manning's arrival.
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