The bus was empty at the time but was being used to transport Juventus fans to the game in Turin.
The incident occurred at a service area outside Turin on the A21 highway, according to ANSA news agency reports.
There had been skirmishes between rival supporters before the accident, in which a 28-year-old woman died.
Both clubs announced the postponement of the match on their Web sites.
Their statement said: "Juventus and Parma, with the approval of the appropriate authorities, have decided to postpone the game as a sign of mourning for the incident involving the Parma fan traveling to the Turin stadium.
"Since it was a tragic fatality, the two clubs decided that the conditions were not right to send the teams out onto field."