One crew member survived and the fate of two others was unknown.
Officials said the tanker was carrying 980 tonnes of acrylic acid, a corrosive organic compound that is used in adhesives, paints and polishes.
No leak has been detected, and officials are studying what environmental protection measures may be needed in case there is a leak.
The Japan Coast Guard said it received a distress call from the chemical tanker Keoyoung Sun on Wednesday, saying it was tilting while seeking refuge from the weather near Japan's Mutsure Island, about 1000km from Tokyo.
The ship was completely capsized by the time rescuers arrived at the scene.
Footage on Japan's NHK television showed the ship lying upside down, a rough sea washing over its red underside.
The ship was carrying 11 crew, of whom nine had been found, authorities said.
The one crew member confirmed alive is from Indonesia, and the coast guard was still searching for two more.
South Korean officials held a meeting on Wednesday to discuss the capsizing.
During the meeting, Vice-Foreign Minister Kang Insun asked officials to mobilise all available resources to support rescue works and assist the relatives of South Korean crew members, according to the foreign ministry.
The ship was on the way from the Japanese port of Himeji to Ulsan in South Korea, the coast guard said.
Its captain was South Korean, and its crew included another South Korean national, a Chinese national and eight Indonesians, according to the coast guard.
Acrylic acid is also used in plastics, resin and coatings, and can irritate the skin, eyes and mucous membranes.
No other details, including how the ship capsized, were immediately known.
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