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The attack took place on Friday in a village in Barga, in Yatenga province, close to the border with Mali.
An investigation has been launched to establish who was responsible for the killings.
Burkina Faso's prosecutor Lamine Kabore did not provide details about Friday's attack but said those injured were being treated in hospital.
"My office was alerted about the seriousness of some of the facts. I therefore gave instructions to the investigation unit to carry out investigations in order to illuminate the said facts and hear all the people who are involved," he said.
The killings took place in an area overrun by Islamist groups linked to al Qaeda and Islamic State.
The groups have been blamed for multiple attacks which have left thousands dead and displaced an estimated two million people over six years.
Earlier this month, militants were accused of killing at least 44 people in the north-eastern province of Seno.
However, members of Burkina Faso's military have also been accused of killing civilians in the country, where the government is said to control less than 50% of the nation's territory.
News of the massacre comes amid growing concern about violence elsewhere in Africa, in Sudan.
Read more on Sudan crisis:
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Burkina Faso's government recently announced it was opening a probe into allegations of human rights abuses by security forces after a video surfaced appearing to show seven children being executed.
Mucahid Durmaz from Verisk Maplecroft, a global risk intelligence firm, said the army had been struggling with controlling its own troops and militias in the country.
He said: "The junta is struggling to convince the public that it will uphold its main promise of improving security.
"The junta's counter-terrorism strategy risks triggering a series of extrajudicial civilian killings in rural areas, due to the loose chain of command and ill-disciplined volunteer militia groups."