Most of the workers were Indian and from the state of Tamil Nadu. It is thought they died from smoke inhalation, local media reported on Sunday.
At least seven people were taken to hospital suffering from severe burns sustained in the fire, medical sources said.
The fire, possibly caused by an electrical short-circuit, broke out around 2.30am local time in the city's Qudaibiyah area, one of the most densely populated areas of the capital with a high concentration of Indian and Filipino workers.
Police said about 200 people were believed to have lived in the building, however some workers said that more than 350 Indian nationals were living there.
The small kingdom of Bahrain, like many Gulf Arab states, relies on a large number of foreign workers - mostly from Asian countries - who work mainly in the construction and the service industries.