The plane took off from southern Spain just before 15:00 Swedish time and was on its way to Cologne in Germany but continued northeast.
German Bild writes that they lost contact with the plane when it was over France.
Fighter jets from several countries went up to try and observe who was flying the plane.
But couldn't see anyone in the cockpit or in the cabin.
At 19.20 the plane passed the southern tip of Gotland and ten minutes later it began to decrease in speed and lose altitude.
When the plane flew into Swedish airspace outside Gotland, Swedish rescue services were called in.
"Mayday relay, mayday relay, this is Sweden rescue", the rescue service alerted ships nearby.
Hear the alarm in the clip above.