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.
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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.
Read more: What is the Kaesong industrial complex?
South Korea is to suspend operations at a jointly-run industrial park in North Korea following the North's recent rocket launch and nuclear test.