Menzies compiled a 48-48 record after taking over for Chris Beard in 2016. The school didn't qualify for the NCAA Tournament during Menzies' time at the helm.
UNLV went 17-14 this season, finishing tied for fourth in the Mountain West standings. A 63-55 loss to San Diego State in the quarterfinal round of the Mountain West Conference tournament eliminated the Runnin' Rebels from the postseason.
"I want to thank Coach Menzies for calming the waters and building a strong foundation for our men's basketball program over the past three years," UNLV director of athletics Desiree Reed-Francois said in a statement. "A change of this significance impacts many good people. It was not taken lightly. Ultimately, after a thoughtful and methodical review, I felt a new direction was necessary for the long term, best interests of the program and our athletics department."
The 57-year-old Menzies previously served as head coach of New Mexico State from 2007 to 2016. He led the Aggies to five NCAA Tournament appearances, five Western Athletic Conference (WAC) tournament championships, and three WAC regular-season titles. Menzies was named WAC Coach of the Year in 2015.