State broadcaster TBC Taifa said 57 people were killed and 65 injured.
Video clips from the accident scene circulating on social media showed the charred remains of dozens of young men. Footage from before the explosion showed a large crowd collecting liquid from puddles in yellow jerry cans after the vehicle crashed.
"The situation is really bad. Many people died, here even those who were not stealing fuel because this is a busy place," Daniel Ngogo, an eye witness, told Reuters.
"The fire was huge and it was challenging to rescue victims. I have seen about 65 to 70 people being rescued because the fire was fast spreading across the accident area."
The explosion occurred in Morogoro, a settlement around 200 km (120 miles) west of the capital Dar es Salaam.
"We have been saddened by reports of an accident involving a fuel truck in Morogoro, which caught fire and burnt several people," government spokesman Hassan Abbasi said on Twitter.