Norfolk Fire and Rescue Service said the plane came down at Hardwick airfield near Bungay at about 15:35 BST.
It burst into flames and firefighters called to the scene found one person had died, a spokeswoman said.
The male pilot was airlifted to Norfolk and Norwich Hospital for treatment and is in a serious condition.
The spokeswoman added: "When the first appliance arrived it was confirmed that [the aircraft] was on fire and unfortunately we have had it confirmed that there was one deceased and one airlifted to hospital.
"As far as we are aware it was two people on board and we believe it was a two-seater plane."
Charles Christian, who lives near the airfield, was out walking when he thought he saw the plane come down.
He said it appeared to come into the runway normally, with its landing gear down and ready to land, but that he heard a small explosion after it disappeared behind some trees, a noise he thought was just the engine playing up.
Mr Christian said: "I was taking the dogs for a walk and I was walking up the back field and the plane in question was flying in and coming into land quite normally and flew right over my head.
"It flew on toward the runway, which is about a quarter of a mile away, and disappeared behind the trees to land.
"Normally when that plane lands they cut off the engine so you sort of hear it backfiring, a spluttering noise, and then it grinds to a halt.
"It was noticeable that this time there was the spluttering noise and then it stopped very quietly and then a few seconds later there was another bang, which I am guessing was the explosion."
Norfolk Police said Denton Road remained closed for investigations to be carried out and that local diversions were in place.
A man in his 80s has died after the light aircraft he was a passenger in crashed in Norfolk.