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Seoul said all operations at the complex would halt, to stop the North using its investment "to fund its nuclear and missile development".
Kaesong is one of the last points of co-operation between the two Koreas and a key source of revenue for Pyongyang.
It came as Japan imposed new sanctions against the North following the launch.
They include a ban on North Korean vessels coming into port in Japan and on vessels from other countries that have visited the state,
The US warned on Tuesday that the North could soon have enough plutonium for nuclear weapons.
South Korea, the US, Japan and others see Sunday's rocket launch - ostensibly to put a satellite into space - as cover for a banned test of missile technology.
Tensions have risen over the past month since North Korea carried out a fourth nuclear test in early January.
"All our support and efforts... were taken advantage of by the North to develop its nuclear weapons and missile programmes," the South's Unification Minister Hong Yong-pyo told reporters.
The announcement came amid reports that the North's military chief, Ri Yong-gil, had been executed on corruption charges.
South Korea's state news agency Yonhap quoted unnamed sources saying the general, who was appointed in 2013, had been deemed guilty of corruption and pursuing personal gains.
There was no confirmation of the report.
Reuters news agency also reported the execution but did not identify its source or how the information had been obtained.
Joint industrial complex located inside North Korea just across from the demilitarised zone
Launched in 2004 - it is a source of badly-needed cash for the North
124 companies operate there from industries including clothing, textiles, car parts and semiconductors
South Korean firms pay about $100m (£69m) a year in wages - about 54,000 North Koreans work there
Last shut down in April 2013 - for four months - after US-South Korean military drills angered North Korea
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