It will be the first meeting between the two programs, as well as the first time Michigan coach John Beilein, who left West Virginia in 2007, will face his former employer.
Bob Huggins replaced Beilein and has since led the Mountaineers to four straight NCAA tournament appearances, with the Mountaineers in contention for another tournament berth this season.
"Playing in the new Barclays Center will truly be a great opportunity for us," Beilein said in the announcement. "Michigan has such a strong alumni base in New York City and surrounding areas that we could not turn down the chance to play in front of them."
"I have many fond memories of my time at West Virginia. Facing them and [Huggins] will give Michigan another opportunity to play against one of the very best teams in college basketball today," he added.
Chantel Jennings writes about Michigan athletics for WolverineNation.com.