It did not give the value of the stolen coins but Yonhap News agency cited unnamed industry sources saying about coins worth about 40 billion won ($37 million) were lost.
Enthusiasm for virtual currencies has waned partly due to a string of cyber heists, including the almost US$500 million theft from Japanese exchange Coincheck Inc.in late January.
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Coinrail is still determining how much was stolen, but the attackers may have looted as much as $40 million, according to observers who point to a digital wallet that appears to be involved in the hack.
Bitcoin was trading at around $6,750 in early afternoon trading in Asia.
Global policy makers have warned investors to be cautious in trading the digital currency given the lack of broad regulatory oversight. But the hack added to existing uncertainties in the virtual currency market, and after Coinrail reported losing about 30 percent of its reserves in the attack, bitcoin's price plummeted.
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To protect its other assets, Coinrail said, it moved them to a "cold wallet" that isn't connected to the Internet.
In South Korea, 14 major local cryptocurrency exchanges adopted measures aimed at better protecting users in January this year, including restrictions on creating more than one account.
Some observers pinned the latest retreat on a hack at a South Korean exchange, while others pointed to lingering concern over a clampdown on trading platforms in China. Coinrail only said that it was cooperating with investigators and other exchanges to try and track down the perpetrators and recover the money.
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Coinrail said in a statement on its website that it's reviewing its system due to hacking attempts. "The company wasn't immediately available for further comments".