It was not clear whether the man was a South Korean, the official said on condition of anonymity. The military was still trying to recover the body and investigating the incident, he said.
South Korea’s Yonhap news agency said South Korean guards had called out to the man to return. But he ignored the instructions, jumped into the Imjin River and clung to a buoy to try to float across.
Yonhap quoted a military official as saying the shooting was justified as the identity of the man was unknown and he could have been a North Korean soldier.
South and North Korea remain technically at war as the 1950-53 Korean war ended only with an armistice and it is illegal to cross the border to the North without permission.
Instances of trying to cross the frontier in such a fashion in broad daylight are extremely rare.
South Koreans wishing to travel to the reclusive North, accused by Western countries and defectors of systematic human rights violations, generally make their way through China.
Tens of thousands of North Koreans are believed to be in China and trying to come to the South. About 25,000 have made it to South Korea.
The shooting comes amid a thaw in ties between North and South, with the reopening on Monday of the jointly-run Kaesong industrial zone just over the border in North Korea.
The complex was shut last April by North Korea as it issued daily threats to attack the South and its ally, the United States.
The two sides also plan more discussions to improve the operations of the factory park and to hold reunions of families separated during the Korean War later this month.