The accident occurred at 10:15 am local time (01:15 GMT) when a rope used to tie the 4,400-tonne destroyer to the dock snapped for an unknown reason, the Yonhap news agency reported.
"The sailors appear to have been injured as the rope hit them when it suddenly snapped", a Navy officer said, as quoted by the agency.
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Five officers were sent to local hospitals after the accident, while four others sustained non-life-threatening injuries, the agency reported.
The ship earlier returned to the country after a six-month anti-piracy mission in the Guld of Aden near the shores of Somalia.
