The AFC West side's head coach will undergo an aortic valve replacement next week after being hospitalised during a round of golf in the team's bye week.
Fox told the team's official website: "I sincerely appreciate all of the support from friends, Denver Broncos fans and so many around the league today.
"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."
The Broncos are currently second in their division.