Noah Mwivanda, a senior police officer in Lamu County, said Tuesday's blast happened between the towns of Mararani and Kiunga.
There was no immediate claim of responsibility.
The deadly incident bore the hallmarks of similar bombings blamed on Somalia's al-Shabab armed group, which has previously targeted security forces in the region.
It increases the death toll from homemade explosives in the past three months to 46, with policemen as the majority of fatalities.
Al-Shabab has carried out more than 100 attacks on Kenya since 2011.
It says the attacks are retribution for Kenya sending troops to Somalia to fight them.
Kenya's President Uhuru Kenyatta, who is campaigning for re-election in August, did not immediately comment on the latest explosion.
On Monday, Kenyatta said if re-elected he would "strengthen the Anti-Terrorism Police Unit by acquiring more specialised vehicles to counter and deter the security threats emerging from terrorist groups".
Kenya has managed to stop the frequency of al-Shabab attacks in its capital, Nairobi, and major towns, but human rights groups say the government uses methods such as extrajudicial killings that can fuel revenge attacks.
Source: News agencies