The coast guard said it believed high waves dragged the ship's anchor, causing the freighter to hit a sea wall and sink Tuesday, South Korea's Yonhap News Agency reported.
A coast guard official said an investigation would determine exactly why the ship sank.
The 8,461-ton Cheng Lui 15 had a 19-member crew, 18 Chinese and one Vietnamese, when it went down off the southeastern port of Pohang, the coast guard said.
The coast guard said it rescued eight sailors, all Chinese. The ship's captain is one of the two missing.
Rough seas made the rescue operation difficult, the coast guard said.
Officials also said they were preparing for a possible oil spill because the vessel was carrying about 130 tons of oil and diesel fuel, Yonhap said.
"Some oil spilled from the vessel at the early stage of the accident but there is no more leak," a coast guard official said. "We believe that the oil tank has not been damaged."
The freighter departed from from the Pyeongtaek, South Korea, on Oct. 2 and arrived at Pohang two days later to unload its cargo, the coast guard said. The ship was set to leave for Japan.