According to data from FlightRadar24, the Cessna 551 took off from Jerez in southern Spain at 1.56pm UK time. German news site Bild said that the aircraft was meant to land at Cologne-Bonn airport.
However, it reported pressure problems in the cabin shortly after take off.
Bild added that French and Spanish jets followed the aircraft but couldn’t see anybody in the cockpit or cabin.
A family of three and a pilot were aboard, according to reports.
Flight trackers showed that the aircraft headed northeast at Paris towards Cologne.
However, the plane went past the city and eventually over the Baltic Sea.
German and Danish warplanes shadowed the aircraft as it passed through their airspace.
According to Johan Wahlstrom, a Swedish Maritime Administration official, they were unable to make contact.
NATO jets from the Baltic Air Police mission in Estonia also followed the aircraft, according to a Lithuanian air force spokesperson.
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A Stena Line ferry has also been sent out to help, according to reports.
The Cessna 551 is a 14-metre long single-pilot that is able to carry six to eight passengers and was originally registered in Austria.