It was not immediately clear who the attackers were.
“Bandits ambushed a bus from Mandera that was heading to Nairobi at dawn and killed 28 passengers of the 60 that were in the bus,” the ministry said on its Twitter feed.
Police Spokesman Masoud Mwinyi confirmed the incident.
Tensions have escalated in Mandera County, near the border with Ethiopia and Somalia, in the past year as clashes between clans have displaced hundreds of people.
The region is awash with guns due to its proximity to Somalia, where al Shabaab has been fighting to topple the government, and Ethiopia, from where the armed Oromo Liberation Front has made incursions into Kenya.