The team announced the suspension Thursday, saying it was for a violation of team rules. The team didn't publicly specify the nature of the violation.
Hinton is a redshirt junior with four career starts. He emerged from spring practices as the projected starter after the departure of four-year starter John Wolford.
Cole is a redshirt sophomore who played in three games last year.
In a statement, coach Dave Clawson said the players "made poor decisions and they take responsibility for their actions."
Wake Forest opens at Tulane on Aug. 30, then returns home for games against Towson and Boston College.