Officials in Seoul say the South Korean vessel opened fire when the Northern ship crossed a disputed sea border. The North Korean vessel then fired back.
North Korea insists its ship did not cross the border, and has demanded an apology, according to news agency KCNA.
The two navies have engaged in deadly exchanges twice along their western sea border in the past decade.
The incident comes days before US President Barack Obama visits Asia, with North Korea seeking direct talks on its nuclear programme.
In the North's version of events, a patrol boat was on a mission to confirm "an unidentified object" on the North's side of the border, and while it was sailing back, South Korean ships chased it and opened fire in a "grave armed provocation".
The North Korean vessel "lost no time to deal a prompt retaliatory blow at the provokers", KCNA said. "Much flurried by this, the group of warships of the South Korean forces hastily took to flight to the waters of their side."
Seoul's military has also demanded an apology for the incident.
South Korean officials said none of their troops had been hurt, while the North's boat had been set ablaze before it sailed away.
Northern limit
In October, North Korea's navy accused South Korea of sending warships across their maritime border to stir tensions, and warned that further incursions could spark retaliations.
The communist state's navy said that on one day alone, ships had crossed the boundary 10 times.
South Korea recognises the Northern Limit Line, drawn unilaterally by the US-led United Nations Command at the end of the 1950-53 Korean War, which has never been accepted by North Korea.
In 1999 a North Korean ship was sunk and several vessels from both sides were damaged during an exchange of fire.
In 2002 four South Korean sailors and an estimated 30 North Koreans were killed in a 20-minute battle.
