The tankers were docked at a jetty owned by military-controlled Myanmar Economic Holdings when the blast happened in a suburban area of the city. The cause was unclear.
"We found four bodies so far," said a fire department official at the scene.
The victims were believed to be workers on the vessels.
"I was shocked when I heard the sound of the explosion," said Thein Zaw Htay, a 35-year old helmsman of a nearby boat. "I saw a ball of fire explode into the air from the tanker. The oil burned and flowed into the river."