The soldier bolted from a guard post at the northern side of Panmunjom village in the Joint Security Area, where border guards of the rival Koreas stand facing each other just feet away.
It said an investigation into Monday's event was ongoing.
The North's drills are expected to run from December to April, according to the South Korean military.
While months-long winter drills are routine for the North, authorities in the South said they were on high alert for any possible changes.
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These were the first gunshots fired at the truce village of Panmunjom in 33 years and the first defection of a North Korean soldier since 2007.
A North Korean soldier was shot by his fellow troops as he was defecting to the south across the demilitarised zone but still managed to successfully cross the border. He's just the seventh soldier to defect since 2012, though the third this year.
South Korea's military has strengthened vigilance in the wake of the incident and remains prepared for any situation, the JCS said.
Two North Korean soldiers defected to the South in June after crossing the frontier at another location. More than a million mines are buried inside the zone.
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Since its last ballistic missile launch September 15, North Korea has not conducted any provocations, raising hopes for possible talks on the long-standing North Korean nuclear stalemate.
The defection came during escalated tensions between the North and the South and almost a week after President Trump visited Seoul for his five-country Asia tour.
US President Donald Trump hinted last week that his administration is now in contact with North Korea.
President Donald Trump, meanwhile, delivered a message to North Korean leader Kim Jong Un during a speech last week before the South Korean National Assembly.
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At the time of the defection, the soldier was clad in the Korean People's Army uniform with no weapon, he added. In 1998, a North Korean solider fled to South Korea via Panmunjom. In September the North carried out its sixth and largest nuclear test, of what it described as a hydrogen bomb. All three "reaffirmed their commitment to maintaining maximum pressure on North Korea in an effort to denuclearize the Korean Peninsula", the White House said.