An official at the Gwangju Seobu Police Station said the athlete was under investigation, but did not provide further details.
Yonhap News Agency reported earlier that the athlete, a Rio Olympics bronze medallist in an aquatics event, denied the allegation.
Gwangju, about 330 km (205 miles) south of the capital Seoul, has been hosting the championships, which feature swimming, water polo and diving, over the last fortnight. The meet finishes on Sunday.
On Saturday, a deck at a Gwangju nightclub collapsed, injuring several foreign athletes competing at the World Aquatics Championships, rescue officials said.