After the lorry careered off the road near the central town of Molo, motorbike riders and others descended on the vehicle in the hope of scooping up petrol, witnesses said.
Then the spill caught fire around dusk, engulfing those closest.
Rescuers said someone may have accidentally dropped a cigarette, although there was also a suspicion someone angered at being blocked by police may have started the fire on purpose.
Hundreds were still milling around the site on Saturday evening. Rescuers were helped by people with torches and car-lights.
“My two sons ran home, picked some jerry cans and ran to get some petrol. I tried to stop them but they did not listen, they told me everyone is going there for the free fuel,” a woman said as she was trying to find her missing sons.
The disaster in Molo followed the deaths of at least 25 people in Nairobi when a supermarket caught fire earlier this week.
Local newspapers have criticised the government for poor safety.
After the supermarket blaze, the Daily Nation said Nairobi’s three million inhabitants are served by just one fire station situated close to a traffic-choked business district.