Kim Yong Nam, who is officially leading Pyongyang's diplomatic delegation to the Games, met Moon at a leaders' reception ahead of the opening ceremony in Pyeongchang.
Moon and his wife received their guests one by one and the two men smiled as they shook hands in a relaxed manner.
There was no sign of Kim Yo Jong, the influential sister of the North's leader Kim Jong Un, who is part of Pyongyang's delegation.
On his left lapel, Kim wore a badge depicting the North's founder Kim Il Sung and his son and successor Kim Jong Il, Kim Jong Un's father.
A seating plan for the dinner shown on South Korean television showed Kim Yong Nam seated at the top table, in between Olympics chief Thomas Bach and UN Secretary General Antonio Guterres, and directly opposite US Vice President Mike Pence.