"But our military is keeping a full readiness posture against the possibility of North Korea's provocations", a South Korean official was quoted as saying by the Yonhap news agency.
The soldier, whose rank and identity have not been disclosed, was flown by helicopter to hospital on Monday after his escape to South Korea, during which he was sacked on by four North Korean soldiers.
The hospital will brief media on the soldier's condition at 0630 GMT, she said, without providing details. He then fled across the JSA, with fellow soldiers chasing and firing at him, South Korea's military said, citing unspecified surveillance systems installed in the area.
About 30,000 North Koreans have defected to South Korea since the end of the 1950-53 Korean War, but most travel through China.
An official with the South Korean Joint Chiefs of Staff said the North's border guards fired at least 40 rounds.
If North Korea is proven to have fired shots through the area, this would constitute a breach of the armistice agreement.
Suh said the South had also informed the North on Monday of the soldier and his treatment, via loudspeakers on the border.
A department official said last month that China's Communist Party continues to hold talks and maintain contacts with its North Korean counterpart, describing the two countries' friendship as important for regional stability.
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. It is located inside the 4-kilometer-wide (2 1/2-mile-wide) Demilitarized Zone, which forms the de facto border between the Koreas since the Korean War. Jointly controlled by the American-led U.N. Command and North Korea, the DMZ is guarded on both sides by hundreds of thousands of combat-ready troops, razor-wire fences and tank traps.
Areas around Panmunjom were the site of bloodshed and defection attempts by North Koreans in the past, but there have been no such incidents in recent years.
The North Korean ambassador accused the council of "turning a blind eye to the nuclear war exercises of the United States who is hell bent on bringing a catastrophic disaster to humanity".
From there they can seek sanctuary and organise a flight to South Korea, where defectors are given assistance and prepared for life outside the hermit state.
Rex Tillerson, the secretary of state, was photographed by North Korean soldiers while he stood inside one of the huts during a visit to the DMZ in March.
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