Police in Magdeburg said the plane crashed in thick fog and caught fire between 8.30am and 8.45am.
The aircraft hit the 27-metre high mast of the weather station on top of the Brocken mountain in the Harz region, according to a worker at the station.
The Cessna single engine plane crashed around 150 metres from the mast after hitting it.
The 38-year-old pilot and the passenger died in the burning aircraft, police said,
They were travelling from Rügen to Reichelsheim near Frankfurt am Main to pick up a car.
Visibility around the mountain which is 1,141 metres high, was reportedly 20 metres.
The Brocken mountain plays a significant role in German literature.
Goethe's Faust cites the mountain's summit as the location of witch revelry on Walpurgis Night, April 30th.
And the 19th century author Heinrich Heine climbs the mountain in his book "Die Harzreise" which was published in 1826.