The incident happened Wednesday night in Florida's 2-1 win when Deveaux elbowed Fleischmann near center ice midway through the second period.
NHL disciplinarian Brendan Shanahan announced the suspension on Friday.
Fleischmann was taken to the locker room after the play but returned later in the period. Officials assessed a match penalty to Deveaux for an illegal check to the head that caused injury.
Under terms of the collective bargaining agreement and based on his average annual salary, Deveaux will forfeit $8,513 during the suspension. The money will go to the Players' Emergency Assistance Fund.