Mike Decker, the council's chief clerk, said Thursday that the bill has been held until next month.
The legislation would strengthen regulations on tow-truck operators who jockey to be the first at accident scenes.
The bill was sparked in part by a shooting allegedly involving competing towing companies. The city's reputation has even spawned a Discovery Channel reality show called "Wreck Chasers."
The new plan would require towing companies to take vehicles to lots controlled by the Philadelphia Parking Authority instead of directly to repair shops.
The city already requires police to rotate jobs among companies. But wreck chasers skirt the system by monitoring police radio and even beating officers to crashes.
