The Interior Ministry announced the officer's death today night, saying the attack happened in the village of Karbabad.
It said an investigation into the attack was ongoing as locals said a large security presence had gathered around the area.
The ministry did not elaborate on who throw the bomb, beyond calling it a "terrorist act." Protesters in Bahrain have thrown similar gasoline bombs in skirmishes with authorities.
Bahrain, home to the US Navy's 5th Fleet, has seen low-level unrest since 2011 Arab Spring-inspired protests there by the kingdom's majority-Shiite population seeking more political power from the island's Sunni rulers.