Yahoo Sports’ Adrian Wojnarowski first reported the firing.
Shaw had a 56-85 record in his tenure with the team, including 20-39 this season. Denver has lost six games in a row going into Tuesday night's game against the Milwaukee Bucks. Denver has the third-worst record in the Western Conference.
David Aldridge of TNT reported that Melvin Hunt will be the team's interim coach for the rest of the season.
"I want to sincerely thank Brian for his time with our organization," general manager Tim Connelly said in a statement. "You won’t find a better guy than Brian and he is one of the brightest basketball minds I’ve ever been around. Unfortunately things didn’t go as we hoped, but we know with his basketball acumen that he has a very bright future ahead of him."
Shaw was recently concerned that his players might be giving up on the season.
"I think it's hard to try to lose, try to tank, try to go out there with guys who are competing with you and not compete back," Shaw said to The Denver Post earlier this month. "It's harder to do that than to just put forth the effort in the first place."
Those thoughts seemed to be confirmed when players could be heard saying "1-2-3 ... six weeks!" during a loss last Friday against the Utah Jazz. There are six weeks left in the season.
Shaw was hired after the team let reigning NBA coach of the year George Karl go after a 57-win season.
- Scooby Axson