The wooden Klemm KL25, which is almost 90 years old, belonged to a flying club in Großenhain, Saxony, which has a private collection of historical planes.
“It was one of the oldest licensed planes in Germany, but not the oldest," a member of the society said on Monday.
The 27-year-old pilot, who is a club member, and a 16-year-old passenger were taken to hospital with life-threatening injuries, police said.
The single-engine propeller plane crashed on landing near the end of the club’s open day.
Investigators are now looking for the cause of the accident and checking the weather conditions at the time.
Police estimated the damage to the plane at €300,000.
The wreck of the plane was dismantled on Monday and removed by truck.