German media outlets carried the reports on Monday, describing the attack as a friendly fire incident.
According to Germany's Der Spiegel weekly, the warship fired two missiles at the aircraft, but both the projectiles crashed into the sea because of "a technical defect."
The "Hesse" frigate involved in the incident headed towards the Red Sea earlier this month as means of thwarting Yemen's pro-Palestine operations.
Yemen’s Armed Forces have been targeting Israeli vessels or those bound for the occupied territories’ ports in protest at the Israeli regime's October-present war against the Gaza Strip that has so far killed nearly 30,000 Palestinians.
The forces have vowed to keep up the operations as long as the Israeli regime sustained the war and a simultaneous siege that it has been employing against Gaza.
The German warship opened fire after efforts to identify an unknown drone "were unsuccessful," Defense Minister Boris Pistorius said, adding that the target was "not hit." The aircraft later turned out to be a "reconnaissance drone," he said.
The drone was apparently not related to a United States-led naval coalition that has been similarly operating in the Red Sea to confront the Yemeni operations.
The Frankfurter Allgemeine newspaper said it was "common knowledge that American combat drones are used in the region that have nothing to do with the [US-led] operation in the Red Sea."
Spiegel said military officials believed that the incident showed that coordination between allies involved in various missions in the region around Yemen "needs to be improved."