The Civil Aviation Authority of Singapore (CAAS) said the aircraft from the South Korean air force's aerobatic team Black Eagles "skidded and crashed into the grass verge" at the side of the runway and caught fire.
The accident happened as the plane was taking off for the aerial display, which was cancelled.
The Black Eagles were supposed to be the final act of the show that also featured aircraft from Singapore, Thailand, Malaysia, Indonesia and the United States.
"Airport Emergency Service responded to the incident immediately and the fire was extinguished," the CAAS said.
"The pilot sustained light injuries and is being treated.
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