Deputy Chief Cabinet Secretary Koichi Hagiuda said the injuries were not life threatening.
Seven other Japanese were eating together at the restaurant, but Japan's government has not been able to contact them, Hagiuda said.
Gunmen attacked the upscale cafe in the diplomatic area of Dhaka late on Friday and had been holding about 20 hostages, before police poured into the building to try to free those stuck inside. At least two police were killed.
Japanese Prime Minister Shinzo Abe speaks to journalists after a cabinet meeting to talk about Dhaka hostage case which suspected Islamist militants hold dozens of people hostage, at his official residence in Tokyo.
Japan said on Saturday that one of its citizens had been shot and wounded in an attack on a restaurant in the Bangladeshi capital and then rescued.
