The assailants opened fire on the 14-seater vehicle after it ran over the explosive device about eight kilometres (five miles) from the town of Mandera.
“Six people were killed during an attack on a vehicle,” said national police spokesman Bruno Shioso.
“A security operation is underway to get the attackers.”
There was no immediate claim of responsibility for the assault.
A police report said a General Service Unit patrol team, which was on foot and nearby, engaged the attackers, who fled towards the Somali border.
The assailants used guns and rocket-propelled grenades during the assault, it added.
The minibus, which was completely mangled in the attack, was carrying an unknown number of passengers.
Shioso told AFP seven people had survived but had “various degrees of injuries”.
The Mandera region is prone to raids over its long and porous land border with Somalia, where the Al-Shabaab Islamist militant group controls swathes of countryside.
Other regions bordering Somalia are also susceptible to attacks and Kenyan officials are often quick to blame the militants for assaults on its soil.
– Terror alerts –
Kenya has suffered several deadly Al-Shabaab attacks in retaliation for sending troops into Somalia in 2011 as part of an African Union force to oust the jihadists.
Kenya is a major troop contributor to the African Union Mission in Somalia.
In 2015, an attack on a university in Garissa, another region sharing a border with Somalia, left 148 people dead, almost all were students.
Last week, a number of diplomatic missions in Nairobi warned of a possible terror attack targeting foreigners in the capital.
The French and German embassies warned of a possible attack within days, while the United States issued a new security alert warning.
In 2019, Al-Shabaab gunmen killed 21 people at a hotel complex in Nairobi and in 2013 a bloody four-day siege in the capital’s Westgate shopping mall left 67 dead.
AFP