Kang said it was highly unlikely that the mine had been washed into the area by rainfall.
Two soldiers were seriously injured and another suffered minor injuries in the September 21 explosion in the DMZ separating the two Koreas.
Several mines have since been spotted near the blast site as part of an ongoing investigation.
Kang said they were probably laid by North Korea as part of efforts to strengthen its border defences, Yonhap reported.
The minister said on Monday that South Korea would take "appropriate, substantial and corresponding" measures if it was confirmed that a North Korean mine caused the explosion.
He did not specify possible measures.
The incident comes as President Lee Jae Myung seeks renewed dialogue between the US and North Korea.
Last week, Lee called at the United Nations General Assembly for US-North Korean talks to resume and told the New York Times that sanctions could be eased if the North froze development of its nuclear weapons program.
North Korea has stepped up border fortifications since 2024, laying mines and reinforcing fences and anti-tank barriers, according to the South Korean military.
The two Koreas technically remain at war because the 1950-53 Korean War ended with an armistice rather than a peace treaty.
