South Korea has said the joint drill, due to finish on Tuesday, was in response to North Korean nuclear and missile provocations and to show any such developments by Pyongyang can be repelled with "overwhelming force".
The soldier bolted from a guard post at the northern side of Panmunjom village in the Joint Security Area to the southern side of the village, according to South Korea's Joint Chiefs of Staff.
The defector was taken to hospital after being shot by another North Korean soldier, the South's military said.
A North Korean soldier defected to the South after his own military shot and wounded him.
Xi urged South Korea to take a "responsible attitude on THAAD that stands the test of history", Xinhua said.
Moon earlier said the Korea-ASEAN joint community aims to boost exchange between the countries' people, instead of governments.
It wasn't known how serious the soldier's injury was.
In a letter sent to Democrats on November 7, Jouas wrote: 'The 28,500 U.S. Armed Forces personnel in South Korea are vastly outnumbered by North Korean forces, as well as [South Korean] forces that will conduct the overwhelming majority of the fighting.
North Korean soldiers have occasionally defected to South Korea across the border. The last time a soldier crossed was in 2007, and before that in 1998. More than a million mines are buried inside the zone.
"I think then the outcome is nearly certain that North Korea will get nuclear weapons and not just North Korea since they'll sell to anybody with hard currency, Iran, terrorist groups, other aspiring nuclear powers". This makes the area a popular stop for visitors from both sides.
After talks in Vietnam on the sidelines of the Asia-Pacific Economic Cooperation forum, Moon and Xi announced on Saturday they will meet in Beijing next month. The attack prompted Washington to fly nuclear-capable B-52 bombers toward the DMZ in an attempt to intimidate North Korea. From January to August 2017, 780 North Koreans escaped to South Korea, according to officials in Seoul.
The UN Security Council has unanimously ratcheted up sanctions on North Korea over its nuclear and ballistic missile programs since 2006.