The exercise required the aircraft to neutralise mobile surface-to-air missile systems and anti-aircraft guns with bombs before carrying out evasive manoeuvres to avoid heat-seeking missiles.
Officials said around 30 bombs were dropped on the correct targets as part of the exercise.
The MK-82 bomb is designed to destroy buildings, bridges and other infrastructure and can leave a crater 7.6m wide by 2.4m deep. Typically, a single bomb can kill anyone within an area about the size of a football pitch.
“Eight MK-82 general-purpose bombs were abnormally released from an air force KF-16 aircraft, landing outside the designated firing range,” the Air Force said.
“We deeply regret the unintended release of the bombs, which resulted in civilian casualties, and wish those injured a swift recovery,” an air force official told Yonhap News.
“We will actively implement all necessary measures, including providing compensation for damage.”
The air force had set up a committee to look into the accident and assess the damage, the official added.
Military and civilian emergency services are operating in Idong, close to the larger town of Pocheon, with television footage showing badly damaged buildings and other infrastructure.
One resident told Yonhap News that he had been at home watching television when the accident happened.
“I suddenly heard an enormous explosion, like a thunderclap, and the whole house shook. When I went outside, everything was in chaos,” Park said.
An adult social centre director told Yonhap: “A sudden explosion shook the building. The windows shattered, and one of our teachers was injured and taken to the hospital.”
“Fortunately, none of the seniors were hurt, but they were so frightened that we sent them all home,” they added.
Annual joint South Korea-US “Freedom Shield” military exercises are set to begin next week.
The two Koreas remain technically at war since the 1950-1953 conflict ended in an armistice, not a peace treaty.
The United States stations tens of thousands of soldiers in the South, in part to protect Seoul against Pyongyang.
In 2022, a South Korean Hyunmu-2 short-range ballistic missile accidentally crashed into a military golf course in the South’s eastern Gangwon province, after it was fired in response to a North Korean missile launch.
The missile did not explode and no one was injured.