An official with Gyeonggi-do Bukbu Fire Services said out of the eight people wounded, two were seriously hurt on Thursday.
Pocheon is about 40km northeast of Seoul, near the heavily militarised border with North Korea.
South Korea's Air Force said eight 225kg Mk82 bombs from a KF-16 jet fell outside the shooting range during joint live-fire exercises.
"We are sorry for the damage caused by the abnormal drop accident, and we wish the injured a speedy recovery," the Air Force said in a statement.
Residents in the area have protested about the disturbance and potential danger from nearby training grounds for years.
Photographs shared by news agency News1 that it said were from the scene showed a badly damaged house with rubble strewn on the ground next to it.
The defence ministry said earlier on Thursday that South Korea and US forces were holding their first joint live-fire exercises in Pocheon, linked to annual military drills due to start next week.
South Korea and the United States will begin their annual Freedom Shield exercise on Monday, Seoul's Joint Chiefs of Staff (JCS) said.
The joint drills, which run until March 20, aim to strengthen the readiness of the alliance for threats such as North Korea, the JCS said.
This year's drills will reflect "lessons learned from recent armed conflicts" and North Korea's growing partnership with Russia, it added.
"Our planners look across the globe and identify the trends that are changing and we look at how we can incorporate that into our exercises," Ryan Donald, a spokesperson for the US Forces Korea (USFK), told a media briefing on Thursday.
About 70 combined field training sessions are scheduled for this year's exercise, said Lee Sung-jun, a spokesperson for Seoul's JCS.
