Leary suffered the injury Sunday against the Rams and was replaced by Max Garcia, who will start at left guard Thursday against the Cardinals.
"It's a huge loss for us from a leadership perspective," Broncos coach Vance Joseph said. "From a player perspective, it's a huge loss. We have great depth in that room obviously with (Connor) McGovern and Max Garcia being the starters now and Sam Jones dressing on game day. So we'll see how that works out. I feel good about that room."