The ban was posted on Hamas Interior Ministry Web site on Tuesday.
It says the ban seeks "to preserve citizen safety and the stability of Palestinian society's customs and traditions."
Hamas wants to impose a strict interpretation of Islam. Its other efforts have included breaking up mixed couples on the beach and obliging female lawyers to wear headscarves in court.
The group insists compliance with the campaign is voluntary and reflects Gaza's conservative ways, but reports have surfaced of offenders being beaten or arrested.
Gazan women almost never drive motorcycles, and rarely even ride behind men.