"Villagers involved and security personnel who broke the Rules of Engagement will be taken action in accordance with the law", it added.
More than 600,000 Rohingya, who are not recognised by the Myanmar government as one of the country's many ethnic groups, have fled to Bangladesh since August past year, when violence between armed Rohingya and Myanmar security forces prompted a severe crackdown.
The massacre took place on September 2 in the village of Inn Din in Rakhine state, the Facebook post said, as tensions escalated pitting Rohingya against security forces and ethnic Rakhine locals following the killing of a Rakhine man.
Asked about Wednesday's statement from the military, her spokesman Zaw Htay said Myanmar was committed to following the rule of law and took allegations of abuses seriously. There, the villagers dug a pit and told the men to enter it.
The village of Inn Din previously featured in a chilling report by Amnesty International, which contains eyewitness accounts from seven villagers who described how vigilantes and the military looted and burned homes and shot people as they fled.
"Some villagers from Inn Din village and security members confessed they killed 10 Bengali terrorists", the office said in its post, using a pejorative term for Rohingya and blaming militants for causing the unrest in the village.
The Myanmar government - headed by one-time democracy icon Aung San Suu Kyi - has been accused by the USA and the United Nations of "ethnic cleansing" in the military crackdown on Rohingya.
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It was a rare acknowledgment of wrongdoing by the Myanmar military during the operation it launched in northern Rakhine in response to Rohingya militant attacks on August 25.
Last month Doctors Without Borders said at least 6,700 Rohingya were killed in the first month of the army crackdown on rebels in Rakhine - the highest estimated death toll yet of violence that erupted on August 25. The Myanmar government has consistently denied all accusations.
They were arrested a month ago under the draconian Official Secrets Act after they were allegedly given classified documents by two policemen over dinner.
The EU and Norway said in a statement issued in Yangon that the killings at Inn Din "confirm the urgent need for a thorough and credible investigation into all violent incidents in northern Rakhine State to ensure the accountability of those found responsible for committing atrocities".
"This grisly admission is a sharp departure from the army's policy of blanket denial of any wrongdoing", said James Gomez, Amnesty's regional director for Southeast Asia and the Pacific, following the military's announcement. Such behaviour shows a contempt for human life which is simply beyond comprehension.
But until now Myanmar authorities have only blamed Rohingya militants for causing a human catastrophe that has left 655,000 of the minority in squalid camps in Bangladesh.
Media access to northern Rakhine State has also been tightly controlled, with most organizations denied access except on heavily supervised military tours.