The Celtic midfielder will miss the remainder of the Scottish league season and could be unavailable for his country's June 8 World Cup qualifier away to Qatar
Ki limped off before the break in the weekend's 3-0 win away to Motherwell, with the Hoops confirming it is a hamstring injury which will rule him out for the remainder of the Scottish season.
However, the injury puts the 23-year-old former FC Seoul man's availability in doubt for the Qatar clash.
The Taeguk Warriors have been drawn in Group A alongside Qatar, Iran, Uzbekistan and Lebanon in the final round of World Cup qualifying through Asia.
South Korea have a bye in the opening round of fixtures, before they open their campaign in Doha.
Ki is a key member of the Korean national team having been only one of three foreign-based players called up for February's crucial qualifier win over Kuwait.