Gunmen stormed the prison in the southeastern city of Owerri after blasting their way in with explosives.
It was among a series of coordinated assaults launched in the early hours of Monday, which also targeted police and military facilities in the capital of Imo state.
Nigerian police have blamed the attacks on the paramilitary wing of a banned separatist movement in the region called the Eastern Security Network.
However, the group has denied involvement.
A Nigeria prison spokesman said: "The Owerri Custodial Centre in Imo state has been attacked by unknown gunmen and forcefully released a total of 1,844 inmates in custody."
He added: "Efforts are in top gear to re-arrest the fleeing detainees."
A separate police statement said: "The attempt by the attackers to gain access to the police armoury at the headquarters was totally and appropriately resisted."
The attacks come less than two weeks after a previous wave of violence in the southeastern part of the country, when at least a dozen security officers were killed during assaults on four police stations, military checkpoints and prison vehicles.
Large amounts of ammunition was stolen in the raids for which no group has claimed responsibility.
It is among a number of serious security challenges facing President Muhammadu Buhari, including a decade-long Islamist insurgency in the northeast, a spate of school kidnappings in the northwest and piracy in the Gulf of Guinea.