The crash occurred at the Lillinghof airfield about 20 miles northeast of the city of Nuremberg, where up to 5,000 people attended the flight show, German news agency ddp reported.
Five people were seriously injured, while 33 others were slightly injured, of whom 22 were taken to a hospital, a police spokesman said at a news conference. Among those hospitalized was a 7-year-old child.
Police said it was still unknown why the pilot of the roughly 70-year-old biplane - with two wings, one above the other - lost control of the aircraft and sped into a crowd of spectators.
"We have secured the plane and it will be released after an investigation," local police chief Guenther Losse told APTN.
The 68-year-old pilot was not hurt in the incident, ddp reported. But a 46-year-old woman died from her injuries at the airfield.
The flight show was to include stunts by small aircraft and sky divers, helicopter tours and tours with a Russian-built Antonov An-2 biplane, a program posted on the Lauf flight association's website said.