The school confirmed the move Thursday.
The 6-foot-5, 250-pound freshman from Hurst, Texas, was a highly regarded player in coach Brady Hoke's first recruiting class.
Barnett was ranked No. 20 among all tight ends by ESPNU 150 for the class of 2011. He was projected as a future starter because No. 1 tight end Kevin Koger is a senior.
Fellow freshman Tony Posada, an offensive lineman, and junior receiver Je'Ron Stokes, who had three career receptions for 27 yards, also left the program this week.
Stokes didn't appear to be a big part of the plan on offense this fall, as Michigan returns veteran wideouts Roy Roundtree and Junior Hemingway, and younger receivers such as Jeremy Jackson have gotten good reviews during preseason camp.
Information from ESPN.com's Adam Rittenberg and The Associated Press was used in this report.