The two police officers said Saturday that the bus traveling to the capital Nairobi was hijacked 50 kilometers from Mandera town.
The officers say the gunmen singled out non-Muslims and shot them dead.The officers insisted on anonymity out of fear of reprisals because of an order from Kenya's police chief that officers not speak to the media.
One official told Kenya's Daily Nation newspaper that assailants had asked passengers to read out verses of the Koran, before executing those who failed.
Kenya has been hit by a series of gun and bomb attacks blamed on Somalia's al-Qaida-linked al-Shabab militants since it sent troops into Somalia in October 2011.
Authorities say there have been at least 135 attacks since then, including the Westgate Mall attack in which 67 people were killed.
"Mujahideen Youth Movement" more commonly known as al-Shabaab is an extremist, “jihadist” terrorist group based in Somalia.
In 2012, it pledged allegiance to al-Qaeda. As of 2013, the group has retreated from the major cities, but imposes strict forms of “Sharia law” in some rural regions.
Al-Shabaab's troop strength as of 2013 was estimated at 4,000 to 6,000 militants.
In October, Somali troops backed by African peacekeepers recaptured the last major port in Somalia held by the al-Shebab, Al-Qaeda's main affiliate in Africa, removing a key source of revenue for the militia.
The al-Shebab, exported charcoal through Barawe earning at least $25 million a year from the trade according to UN estimates.
Barawe , in the Lower Shabelle region of Somalia, 200 kilometers southwest of Mogadishu was al-Shabab stronghold.