The police vehicle exploded into flames after it was hit by a suspected rocket-propelled grenade as it provided security for a bus near the remote Kenyan town of Elwak, on the border with southern Somalia.
"We condemn the attack by Al-Shabaab, five officers were killed," Mandera governor Ali Roba said.
The killing is the latest in a long line of attacks in Kenya's restive northeast.
The Shabaab, East Africa's long-time Al-Qaeda branch, is headquartered in Somalia where it is fighting to overthrow the internationally-backed government in Mogadishu, which is protected by 22,000 African Union troops, including Kenyan soldiers.