But there was no direct exchange of gunfire between South and North Korean guards in the process.
While on average more than 1,000 North Koreans defect to South Korea every year, most travel via China and it is unusual for a North Korean to cross the land border dividing the two Koreas, which have been in a technical state of war since their 1950-53 conflict ended in a truce, not a peace treaty.
North Korea has not commented on the shooting, but it usually responds angrily to defections and often accuses South Korea of kidnapping its citizens.
The trip will come just a week after US President Donald Trump visited Beijing as part of a lengthy Asia tour, where he pressed for greater action to rein in North Korea, especially from China, with which North Korea does 90 percent of its trade.
The U.S. -led United Nations Command, which oversees the South Korean side of the JSA, said the defector drove the jeep near the de facto border line.
North Korea's Ambassador Ja Song Nam said in a letter to UN Secretary-General Antonio Guterres that this was "the worst ever situation prevailing in and around the Korean peninsula".
The four-day simulated exercises, which will go on until Tuesday, 14 November, will include participation from South Korean naval forces as well.
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"He crossed from a North Korea post towards our [South Korean] Freedom House", the South said in a statement. He was unarmed and wearing a combat uniform for a low rank, with his identity yet to be found, the military also said.
The injured man was airlifted to a hospital south of Seoul, where he was operated on by one of the South's best trauma surgeons.
"He has at least six gunshot wounds on his body and the penetrating wound in the abdomen is the most serious", the doctor, Lee Cook-Jong, told reporters, AFP said. The next 10 days will be crucial for his recovery, Lee was quoted as saying by the Yonhap News Agency.
Trump tried to make a surprise visit to the DMZ last week, but his helicopter was forced to turn back to Seoul after heavy fog prevented it from landing at the frontier.
North Korea warned Monday that the unprecedented deployment of three USA aircraft carrier groups "taking up a strike posture" around the Korean peninsula is making it impossible to predict when nuclear war will break out.
The presence of three U.S. aircraft carriers off the Korean Peninsula is pushing the region closer to nuclear war, according to a North Korean letter to the United Nations secretary-general, CNN reports.
Monday was the first time since 2007 a North Korean soldier had defected across the JSA.