The blaze reportedly broke out early on Friday in an engine room of the Aegean Wind and spread upwards.
The vessel, which was carrying iron ore from Brazil to Texas, was about 160km (100 miles) north of Venezuela, near Margarita Island.
Venezuela's navy helped in the rescue. Five injured people were airlifted and taken to hospital on the mainland.
Admiral Carlos Maximo Aniasi, commander of Venezuela's navy, said the blaze had spread upward on the vessel which had a 24-strong crew.
"Nine bodies were found in different compartments of the Greek ship," he told Venezuelan state media.
The bodies belonged to nine sailors - six Filipinos and three Greeks - reported missing earlier in the day.
Two Philippine nationals suffered third-degree burns on their face and hands and three Greek crewmates had less severe burns, said Rafael Lugo, the national commander of Venezuela's Maritime Rescue and Aid service.
The 10 surviving crew members, including a woman, were on the deck, Mr Lugo told Reuters news agency.
The cause of the blaze was unknown and the Aegean Sea would be towed to Margarita, Adm Aniasi added.