Al Shabab's Radio Andalus said in a broadcast their gunmen killed two Kenyan security forces and injured several others in the attack.
Images shared by the police showed a burned-out truck and a body lying in the sand. Police said they had little information on the whereabouts of other police officers travelling in the vehicle.
The police vehicle was travelling from Hayley Lapsset camp to Garissa town, around 120 km (75 miles) from the Somali border, when it hit an explosive device, police said in a statement on Wednesday.
The militants then fired a rocket-propelled grenade at the vehicle and engaged in a heavy firefight which took the lives of the victims, police said.
Al Shabab has been under pressure in Somalia since August when President Hassan Sheikh Mohamud began an offensive against them, supported by the United States, ATMIS and allied local militias.
The al Qaeda franchise continues to make cross-border raids as part of its campaign to pressure Kenya into withdrawing its forces from Somalia, who make up part of the African-Union mandated peacekeeping force ATMIS.
The group killed 166 people at Garissa University in 2015, and 67 at a mall in Nairobi in 2013, but the frequency and severity of al Shabab attacks in Kenya have reduced in recent years.