Johnson has been one of the Longhorns' most versatile offensive playmakers all season. He has 121 yards rushing and 168 yards receiving. Johnson also returned a punt for a touchdown in Texas' victory over Oklahoma earlier this season.
This is the second time Johnson has been suspended. He also missed the 2012 opener against Wyoming.
Brown also announced fullback Chet Moss would be suspended for the Texas Tech game. The Longhorns are off this weekend.