The pilot survived after the plane suffered a technical fault and came down in the Jizan region, a Saudi-led coalition's statement said without going into further detail, Reutersreported.
Bahrain has taken part in the Saudi-led coalition bombing the Houthi movement for nine months, and scores of ground forces from the United Arab Emirates, Bahrain and Saudi Arabia have been killed since the start of the conflict.
In a separate incident, Bahrain's official news agency BNA reported on Tuesday that three of its servicemen were killed along Saudi Arabia's southern border in an accident, without providing any more details.
Mostly Persian Gulf Arab forces intervened in a civil war in Yemen on March 26 after the Houthis ousted the government in a revolution against corrupt officials beholden to Saudi Arabia and the West.
The Saudi-led aggression has left almost 7,000 people dead and plunged the already impoverished country into a humanitarian crisis.