One of the injured policemen is in a “critical condition” in hospital after the attack late on Thursday night, an Interior Ministry spokesman was quoted as saying.
The vehicle was attacked in Sitra, a town some 7.5 km southeast of Manama, at about 19:00 GMT. It was carrying 12 policemen.
Reports in the local media, which could not confirmed with government officials as Friday is the weekend, gave no indication of who the attackers might be.
Bahrain was hit by a wave of violent unrest in the mid-1990s as members of the island's Muslim Shia community led a campaign for political rights and social advancement.
Shias form a slight majority of Bahrain's approximately 400,000 citizens, but the ruling family is Sunni.
The strife faded toward the end of the decade and the king, Shaikh Hamad bin Isa Al Khalifa, restored democratic elections.
Bahrain hosts the base of the US Navy's 5th Fleet and gave tacit support to the US-led invasion of Iraq earlier this year.