A report by the BBC said detective inspector Titus Phiri was arrested after releasing the suspects from Leonard Cheelo police station in the capital, Lusaka, before running away himself.
The 13 detainees were accused of crimes such as assault, robbery and burglary.
They are all currently on the run and a manhunt has been launched to find them.
Police spokesperson Rae Hamoonga said that Phiri, “in a state of intoxication, forcibly seized cell keys” from constable Serah Banda on New Year’s Eve.
“Subsequently, Detective Inspector Phiri unlocked both the male and female cells and instructed the suspects to leave, stating they were free to cross over into the new year,” he said.
“Out of the 15 suspects in custody, 13 escaped. Following the incident, the officer fled the scene.”
Mr Phiri has not yet commented on the allegations.
Reacting to the incident, former presidential spokesperson and lawyer Dickson Jere wrote on Facebook: “I keep laughing each time I picture the scenario – comical! But then, I remembered a similar incident in 1997.”
On New Year’s Eve in 1997, the late, controversial High Court Judge Kabazo Chanda ordered the release of 53 suspects, some of whom were deemed dangerous by the police.
Mr Chanda was annoyed that the suspects had been arrested as long ago as 1992, but had not yet appeared in court.
“Justice delayed, is justice denied,” he said.
