The Austrian-registered Cessna 551 aircraft was flying from Jerez in southern Spain, from where it took off at 1256 GMT. without a set destination, according to the FlightRadar24 website.
It turned twice, at Paris and Cologne, before heading straight out over the Baltic, passing near the Swedish island of Gotland. At 1737 GMT it was listed on the tracker as rapidly losing speed and altitude.
"We've learned that the plane has crashed (in the ocean) north-west of the town of Ventspils in Latvia," a spokesperson for Sweden's rescue service said. "It has disappeared from the radar."
German and Danish warplanes had earlier been sent to inspect the aircraft as it passed through those countries' airspace, but were unable to make contact, Johan Wahlstrom of the Swedish Maritime Administration said.
"They could not see anyone in the cockpit," he said.
German newspaper Bild reported that a man, a woman and their two daughters were aboard, without sourcing the information.
A Lithuanian air force helicopter was dispatched to the crash site for search and rescue at neighboring Latvia's request, a Lithuanian air force spokesperson said.
"Our ships are on the way to the position where the plane crash happened," Liva Veita, spokesperson of the Latvian Navy, told Reuters.
A Stena Line ferry traveling from Ventspils to Norvik in Sweden has also been redirected to the crash site, according to the MarineTraffic website. The website also shows a Swedish search and rescue helicopter and airplane at the site.
NATO fighter aircraft earlier took off to follow the plane, a Lithuanian airforce spokesperson told Reuters. The Swedish rescue service said they had reported that no one was visible in the Cessna's cockpit.
The fighter aircraft were from the NATO Baltic Air Police mission in Amari airfield in Estonia, the Lithuanian airforce spokesperson told Reuters.
The mission in the airbase currently consists of four Eurofighter jets of the German Air Force, according to NATO. The spokesperson did not say how many jets there were or comment further.