Mays fractured the fibula just above his left ankle while blocking for punt returner Trindon Holliday in the fourth quarter Sunday night when a Saints player inadvertently leg-whipped him.
Coach John Fox said it's doubtful Mays was a candidate to be placed on recallable injured reserve "just because of what's left in the season."
"We're going to miss Joe," linebacker Wesley Woodyard said. "Things definitely aren't going to be the same without having him out there, his presence, his leadership and his ability to go out there and make plays."
Mays has had a rough season since signing a three-year, $12 million deal in the offseason. He was suspended for a game and docked $50,000 for an illegal hit on Houston QB Matt Schaub and lost his starting middle linebacker job two weeks ago to veteran Keith Brooking following a poor performance by the defense in a 31-21 loss at New England.
That relegated Mays, who was making $4.5 million this season, to special teams duty. But he maintained his locker room leadership, teammates said.
"He didn't get down on himself. He continued to pick his teammates up and that's one thing you look for as a good teammate, whether throughout the tough times whether you're going to be the same person or you're going to be a different person," Woodyard said. "He was sad but he continued to work hard every day and he came out here and pushed everybody else, and that's the big thing we were proud about."
Brooking, in his 15th season, said he spoke with Mays after the game and told him about how he went on IR his third year in the league with a foot injury and missed 11 games but returned the next season and "I haven't missed a game since."
"You hate to lose a guy that we were all counting on. He's been a very big part of this football team," Brooking said. "The main things are for him just to keep his head up, keep fighting, believing and don't allow this to get him down. More than anything, it's just motivation for him to come back even better than he was before."
The team's leading tackler in four of the last five seasons, Williams is serving an NFL-mandated three-game ban over his August conviction for driving while ability impaired. This is on top of the six-game suspension he completed for violating the NFL's policy on performance-enhancing substances. He's eligible to return for the Broncos' game Nov. 18 against San Diego.
"It's always good to have a guy that can roll in," said Woodyard. "D.J., with his experience, that allows us to be able to play a lot of different things and do a lot of different things with him."