Coach Gary Kubiak says Tate will be placed on injured reserve and undergo surgery this week.
The 5-foot-11 Tate hurt his right ankle in Saturday's 19-16 loss to Arizona and was carted off the field. Kubiak said Sunday that the injury was "pretty severe."
Kubiak said team doctors expect Tate to fully recover.
"The surgery should be fine, he should be back playing next year," Kubiak said. "But it's a big blow. We were counting on him a great deal. He's a dang good-looking young player."
Kubiak said he and general manager Rick Smith will be watching for free-agent running backs to become available.
"Having four guys right now, our eyes are open," Kubiak said. "We've got a lot of preseason football left, so Rick and I have to look around and see what's happening. We have to get these four guys ready to play. They all need a lot of time."