The 63-year-old member of a Seoul-based conservative civic group stabbed himself in the abdomen around 11:53 a.m. while holding a protest at Gimpo International Airport, they said.
Kim was taken to a nearby hospital for non-life threatening injuries, they added.
The delegation, led by former Japanese Finance Minister Fukushiro Nukaga, entered the country to meet with South Korea's incoming President Park Geun-hye amid concern that the already strained relations between the neighboring countries could worsen under the right-wing Abe.
Kim previously rammed a truck into the Japanese embassy here in July of last year to demand the arrest of a right-wing Japanese activist who set up a provocative wooden stake beside a bronze statue of a young girl in front of the Japanese embassy. The statue represents the South Korean women who were forced into sexual slavery by the Japanese Army during World War II.