The accident occurred when a small petrol tanker overturned at 9:30 am (0630 GMT) on a downhill slope in the city centre, where dozens of cars had halted near a traffic light.
The driver of the truck lost control of the vehicle and jumped out as it overturned, spilling its lethal content on the street.
The spilt fuel then ignited nearly 20 cars leaving their occupants trapped inside.
Most of the dead were burnt beyond recognition, a civil defence source said, adding that the toll could still rise. The dead included three little girls.
Interior Minister Koftan Majali immediately rushed to the scene of the blaze, telling reporters that the incident was “not a terrorist work but an accident that can happen anywhere".
Witnesses said the fuel caught fire and spread to cars waiting further down the hill, as well as those passing by or parked on the street.
The accident took place across the street from a tobacco factory and down the hill from several five star hotels, foreign embassies and ambassadorial residences.
A huge mushroom of black smoke billowed over the area and could be seen from different neighbourhoods in Amman, which is built on seven hills.
It alarmed residents in the capital, which has been on edge as Jordan on Wednesday hosted a summit between US President George W Bush and the Israeli and Palestinian prime ministers.