Shin Tae-yong's side lost their first two games in Russia, but still have a chance of advancing providing they defeat the world champions and Mexico beat Sweden.
However, they will have to do so without one of their stars after it emergged that Ki will sit out Wednesday's game in Kazan due to a calf injury suffered in the defeat to Mexico on Saturday.
According to quotes picked up by 'Yonhap News' on Sunday, a Korea team official said: "A medical inspection at a hospital showed that Ki damaged his left calf muscle.
"He needs two weeks of treatment."
The same report claimed that the Swansea midfielder left the stadium on crutches after picking up the problem.
The injury comes as a major blow to the Koreans as they look to spring a huge surprise by coming back from the dead in the 'group of death'.