Tigray leaders, who are fighting the federal forces and their allies, said the victims of the arson were ethnic Tigray, describing the incident as brutal.
The Ethiopian authorities said they would prosecute anyone seen in a videotape showing armed men burning at least three people alive.
The video, which has spread widely on social media since Friday, sparked outrage among many in the country, which is facing an ethnic conflict.
The Ethiopian Government Communications Service confirmed that the incident - in which armed men attacked and burned three civilians - took place in Guba, in the northwestern Benishangul-Gumuz region.
She added, "The video that was circulated on social media shows a horrific and inhuman act, and that whatever their motives, the government will prosecute the perpetrators of the heinous crime".
The authorities did not say when the incident occurred, and it was not immediately clear whether any of the suspects had been arrested.
Tigray leaders, who are fighting federal forces and their allies, said the victims of the arson were ethnic Tigray, and described the incident as brutal, in a statement issued Saturday.
They also accused "the expansionist sons of Amhara and their comrades" of committing atrocities against the Tigray residing in Benishangul-Gumuz.
It is noteworthy that both sides of the Tigray conflict are accused of human rights violations.
The Ethiopian Human Rights Commission appointed by the government, on Friday, accused the Tigray forces of killing civilians indiscriminately and shelling towns extensively since August during their invasion of the Amhara and Afar regions.
Prime Minister Abiy Ahmed's government is struggling to contain the ethnic attacks that have spiraled out of control in recent months, especially after the outbreak of the Tigray War in November 2020.
It is believed that thousands of civilians have been killed in the ongoing conflict in some areas of the country, including the northeastern Afar region.
Abiy came to power in 2018 and made major political reforms that led to him being awarded the Nobel Peace Prize the following year.
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- Agencies