The incident took place late in the second period of the Blues' 2-1 overtime win over the Stars on Wednesday night, leaving Morrow with a cut near his left eye. Pronger was assessed a minor penalty.
Pronger was suspended for one game last season and is considered a repeat offender under terms of the collective bargaining agreement. He will forfeit $231,70.32 in salary.
Pronger will miss games against Chicago on Friday and Colorado on Sunday.