The vehicle was carrying seven officers when it drove over the device in the southeastern town of Baure.
"We have lost four officers in this attack that also killed another person. The vehicle drove on an IED (improvised explosive device)," a senior police officer in the coastal Lamu district near the Somali border, told AFP on condition of anonymity.
It was not immediately clear if the fifth person, a civilian, was in or near the vehicle at the time.
According to a police report seen by AFP, the vehicle was carrying seven officers when it drove over the device in the southeastern town of Baure.
Two of the officers are missing.
Last week 14 officers were killed in three separate blasts involving roadside bombs in different regions of northeastern Kenya along the border with Somalia.
The Shabaab, a Somali-led jihadist group linked to Al-Qaeda, claimed responsibility for the attacks.
Inspector General Joseph Boinnet of the Kenyan police warned more attacks were likely during the holy month of Ramadan.
Since 2007, the Shabaab has fought to overthrow successive internationally-backed governments in Somalia but began attacking Kenya in 2011 after Nairobi ordered its troops into Somalia to fight the militants.
Kenyan soldiers are now part of a 22,000-member African Union mission fighting there.
In 2013, Shabaab gunmen raided a shopping mall in the capital Nairobi killing 67 people, and in 2015 a similar attack on a university in Garissa left 148 dead.