The aircraft was part of the Black Eagles, an aerobatic team belonging to the South Korean Air Force, which was set to perform a flying demonstration at the Singapore Airshow.
At about 1:24 p.m. HK/SIN, the aircraft "skidded and crashed into the grass verge" at the side of one of the runways, and caught fire, the Civil Aviation Authority of Singapore said in a statement.
The pilot was being treated for "light injuries," the civil aviation authority said. Meanwhile, the affected runway was closed until further notice.
Changi Airport, in a separate Facebook post, said that emergency services put out the fire. It later said a number of flights would be delayed for the next several hours.
When CNBC visited the Black Eagles' booth at the airshow, it was empty and no personnel were around to provide any updates on the incident.
Several security personnel on ground at the airshow said they weren't aware of the crash.
Meanwhile, South Korea's Yonhap News reported that the country's air force said that an investigation was launched to understand the cause of the accident and potential damage.