Bahrain's military made the announcement yesterday in a statement carried by the state-run Bahrain News Agency.
It says Capt Ahmed Mohammed Ameen, Capt Mubarak Saad al-Rumaihi, and 1st Sgt Hassan Ali Eskandar Majid were killed on Saudi Arabia's southern border.
The statement said other soldiers were wounded, without elaborating. Cross-border fire from the conflict has killed soldiers and civilians in the past.
A Saudi-led coalition backing Yemen's internationally recognized government has been battling the Shiite rebels, known as Houthis, since March.