"I've decided not to seek a second term," Huh, 55, told journalists.
"My family members suffered a lot ... I want to have time to recharge myself and spend some time with my family," said Huh whose 30-month coaching contract expires with the end of the World Cup.
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The Korea Football Association Chairman Cho Chung-Yun said earlier he had wanted Huh to remain in the job after he successfully guided South Korea through to the final 16 where they were eliminated by Uruguay.
It was South Korea's best performance at any World Cup finals held on foreign soil.
In the group stages South Korea beat Greece 2-0 but suffered a crushing 4-1 defeat to Argentina, which sparked a barrage of cyber attacks on the coach notably over his decision to shuffle his defenders by bringing on Oh Beom-Seok for Cha Du-Ri.
Cha performed well in the match with Greece but Oh made some decisive errors, contributing to Argentina's overwhelming victory.
After holding Nigeria to a 2-2 draw in their final group B match, South Korea advanced to the last 16. But they were defeated 1-2 by Uruguay in the first knockout stage match.
Huh's wife, Choi Mi-Na, told the Chosun Daily that she and their children had been deeply wounded by hurtful Internet postings.
"I told him he should quit ... The coach and all my family members have been hurt enough," she said.
