The precise causes of the blast on Monday were not clear.
It happened when a crowd flocked around the tanker as it headed to resupply a petrol station in the Bent Bayyah district, TRT reported.
A stampede occurred, followed by a massive explosion that set several cars on fire, according to images posted online.
An official at the main hospital in Sebha, southern Libya's main city, said six people had died.
The hospital's management said on Facebook that "more than 50 wounded were admitted to Sebha hospital", without indicating the number of deaths.
Many of the wounded were in a critical state, said a security source in Sebha, hundreds of kilometres south of the capital Tripoli.
Interim Prime Minister Abdulhamid Dbeibah tweeted that his government was "closely following" the incident.
"We have ordered a crisis cell to urgently transfer the wounded to major hospitals," he said.
Libya has Africa's largest proven oil reserves, but chronic corruption and theft for smuggling to neighboring countries mean that the pumps often run dry.
Southern Libya is particularly affected by poor services and a lack of investment, more than a decade since the overthrow of longtime ruler Muammar Gaddafi in a 2011 uprising.