Nineteen more people were hurt, three of them seriously, in Saturday's blast, the communications ministry said.
Education Minister Stanislas Ouaro said the bus was using a road that was supposed to be closed to traffic because of the risk of attacks in the region near the border with Mali.
No group said they planted the bomb but militant violence in Burkina Faso has been blamed on militants linked to both Al-Qaeda and Islamic State groups.
Ouaro said the dead were among around 160 passengers aboard three buses carrying 104 students.
The explosion happened in Sourou province, a security source said, telling AFP: "The vehicle hit a homemade bomb on the Toeni-Tougan road."
Meanwhile, the army reported an assault against gendarmes at Inata in the north on Friday, saying "a dozen terrorists" had been killed.
The deaths came after 35 people, most of them women, died in a massacre on December 24 in the northern city of Arbinda and seven Burkinabe troops were killed in a raid on their army base nearby.
The Islamic State in West Africa (ISWAP) said it had attacked the military base but made not mention of the Arbinda massacre.
Burkina Faso, bordering Mali and Niger, has seen frequent militant attacks which have left hundreds of people dead since the start of 2015 when Islamist extremist violence began to spread across the Sahel region.
In a televised address on Tuesday, President Roch Marc Christian Kabore insisted that "victory" against "terrorism" was assured.
The entire region is fighting against a militant insurgency with help from Western countries, but the bloodshed has continued.
Burkina Faso, Mali, Mauritania, Niger and Chad have joined forces to combat terrorism in the fragile region that lies between the Sahara and the Atlantic.
Increasingly deadly Islamist attacks in Burkina have killed more than 750 people since 2015, according to an AFP count, and forced 560,000 people from their homes, UN figures show.