It happened when a crowd flocked around the tanker as it headed to resupply a petrol station in the Bent Bayyah district. 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, told AFP 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 kilometers south of the capital Tripoli.
The precise causes of the blast were not clear.
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 neighbouring countries means 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 dictator Moamer Kadhafi in a NATO-backed 2011 uprising.