One blast on Thursday killed "three volunteers for the defense of the nation" on a road in the northeast near the border with Mali and Niger, it said.
Another explosion on Wednesday claimed the lives of six soldiers on patrol in another area near the Niger border on Wednesday, the same source added.
Unidentified attackers also blew up a bridge on the same road, the source said.
Over the past weeks, jihadists have been trying to blow up bridges on routes leading to main towns in the north of the country, the Burkinabe army says.
Attacks using improvised explosive devices have been on the rise since 2018 in Burkina Faso, and have killed almost 400 people, according to an AFP tally. They are often followed by ambushes.
Jihadists based in neighboring Mali began mounting cross-border raids on Burkina Faso and neighboring Niger in 2015.
In Burkina, the violence blamed on groups affiliated to Al-Qaeda and the Islamic State group has killed thousands of people and displaced 1.9 million more.
Burkina's ruling junta took power in a January coup that ousted former president Roch Marc Christian Kabore, amid widespread anger at the government's failure to deal with the insurgency.
Today more than 40 percent of the country remains outside the government's control, according to official figures.