Four Cameroon soldiers were searching for a missing colleague on June 1 when they encountered "a group of frenzied villagers", the Defense Ministry said.
They opened fire, killing four women, four men and an 18-month-old girl and slightly wounding a 12-month-old baby, it said.
Cameroon's military said the incident took place in Missong in the Northwest Region.
The ministry statement, in an exceptionally swift condemnation, described the killings as "inappropriate, ill-suited for the circumstances and manifestly disproportionate" and said the troops had been detained pending the outcome of an investigation.
The Northwest and neighboring Southwest Region are home to most of the anglophone minority in majority French-speaking Cameroon.
After years of chafing at perceived discrimination, anglophone militants declared an independent state in the two regions in 2017, triggering a crackdown by the authorities.
The spiral of fighting has claimed more than 6,000 lives and prompted more than a million people to flee their homes, according to the research organization International Crisis Group (ICG).
In February 2020, at least 23 people were killed in a military raid on the village of Ngarbuh in the Northwest Region, 15 of whom were children, according to UN figures.
The army initially said they had died when a fuel tank exploded during a firefight between troops and separatists.
But as an international outcry developed, the authorities said the civilians had been killed by "uncontrolled" soldiers who were supported by militiamen.
Three soldiers were then prosecuted for murder and pleaded not guilty, but the verdict has still to be announced more than two years later.
The Defense Ministry statement Tuesday said it "deeply regrets this grave and unfortunate incident and expresses its deepest condolences to the families of the victims".
"The inquiry that was immediately opened by the local administrative and judicial authorities... will enable full light to be shed and to discern the outlines and responsibilities for this regrettable misunderstanding."
Ilaria Allegrozzi, a researcher on central Africa at NGO Human Rights Watch (HRW) , said the inquiry had to be "credible and independent".