The blasts were set off by a fire in the depot in the city of Maracay, about 100km (60 miles) west of Caracas.
It took firefighters several hours to bring the situation under control.
Officials said the blaze began shortly after 0400 local time (0800GMT), and television pictures showed thick white smoke rising up from the area.
Local resident Yandry Rey said she saw a “ball of fire” after hearing the explosions.
“It seemed as though they were bombing us. It was horrible,” Ms Rey told the Associated Press.
Officials said that firefighters were waiting until the explosions died down before investigating further.