The team made the announcement through their Twitter account.
Mays, 28, had a rough 2012 after signing a three-year, $12 million deal before last season. He was suspended for a game and docked $50,000 for an illegal hit on Houston Texans quarterback Matt Schaub and lost his starting middle linebacker job to veteran Keith Brooking after a poor performance by the defense in a 31-21 loss at New England.
Brooking is a free agent. Second-year linebacker Nate Irving is reportedly a strong candidate to start at middle linebacker this season.
Mays fractured the fibula just above his left ankle while blocking for punt returner Trindon Holliday in the fourth quarter of a Week 8 game vs. the Saints when a New Orleans player inadvertently leg-whipped him.
The Broncos reportedly tried to trade Mays during April's NFL draft but found no takers. He was scheduled to make $4 million this season, according to ESPN.com's John Clayton.
Information from The Associated Press was used in this report.