Jostled by crowds, Ashraf waved before stepping inside the court building.
The apex court had issued the notice Aug 8.
The order said it was unfortunate that the prime minister had failed to implement the court's directives.
The court had July 25 given Ashraf time up to Aug 8 to write to Swiss authorities to reopen corruption cases against Zardari.
Ashraf's predecessor, Yousuf Raza Gilani, was disqualified by the court for contempt after he refused to accept the court's orders.