"There was an ambush on officers who were on patrol and as a result, 13 officers are missing," police spokesman George Kinoti said. "Two others sustained injuries and have been taken to hospital."
Local officials said more than 10 officers may have been killed in Monday night's ambush, while Kenyan media reported the number of dead could be as high as 20.
The attack in Garissa County came just days after extra Kenyan security forces were deployed in the area to strengthen security after a series of raids by gunmen from the Somali-led Al-Qaeda branch.
A female student hostage is escorted out of Garissa University after Kenya Defence Forces ended a siege by terrorist gunmen on April 2, 2015. At least 70 students were massacred when Somalia's Shebab Islamist group attacked a Kenyan university today, the interior minister said, the deadliest attack in the country since US embassy bombings in 1998. AFP PHOTO
Garissa County has remained volatile with numerous attacks since last month when four Al-Shebab militants stormed Garissa University College, killing 142 students and 6 security forces during a day-long siege.
Also last week Shebab militants briefly took control of a mosque in Garissa, delivering a hardline sermon to captive worshippers, before leaving.
Once a Somalia-focussed insurgency Shebab has in recent years turned its attention to Kenya, demanding it withdraw soldiers that were deployed to Somalia in 2011, and launching a series of attacks including the 2013 assault on Nairobi's Westgate mall that killed at least 67 people.