New Zealander Ko was four strokes behind Australia's Green when play was halted just after 1 p.m. at Seowon Valley Country Club due to unplayable conditions.
The second round of the no-cut event is set to resume at 8 a.m. on Saturday, with round three scheduled to begin later in the morning.
Ko was 3-under par for the day after 13 holes, taking her to 8-under overall.
The 27-year-old is aiming to extend a scintillating run of form that saw her win Olympic gold in Paris and end an eight-year major drought at the Women's British Open at St Andrews two weeks later.
Green began the day tied for the lead with South Korea's Jenny Shin and South African Ashleigh Buhai, but she moved out in front after finishing nine holes at 4-under for an overall score of 12-under.
Buhai, who had also completed nine holes, was two strokes back on 10-under.
Ko was joined on 8-under by Shin, South Korean Choi Hye-jin and Denmark's Nanna Koerstz Madsen.
Australia's defending champion Minjee Lee was on 4-under overall after finishing 13 holes at 1-over.
