The three junta-led Sahel neighbours jointly announced in January they would leave the 15-member Economic Community of West African States (ECOWAS), which has sought to persuade them to reconsider their decision.
The West African country faces insecurity and widespread humanitarian needs, making the role of such airlifts crucial to reaching places that are too dangerous to access by road.
The ministry statement did not say how many prisoners had escaped Koutoukale, which lies 50 km (30 miles) northwest of the capital Niamey.
Niger and its military-led neighbours Mali and Burkina Faso signed a confederation treaty on Saturday, signalling an ever-closer alignment between the countries in the insurgency-torn central Sahel.
The Alliance of Sahel States treaty, signed on Saturday, underscored the three countries' determination to turn their backs on the 15-member ECOWAS, which has been urging them to return to democratic rule.
Formalising the treaty to establish a confederation confirms the rejection by Niger, Mali and Burkina Faso of the 15-member Economic Community of West African states (ECOWAS).
The new charter also allows Traore to run for president when the elections take place.
The violence has killed almost 20,000 people and displaced more than two million in a region racked by instability.
With its reputation at stake, ECOWAS's handling of the latest political upheaval - in Senegal - is being closely watched.
ECOWAS' extraordinary session follows Senegal President Macky Sall's sudden decision to delay elections, just a week after Burkina Faso, Mali and Niger declared they were quitting the bloc.
Article 91 of the bloc's treaty stipulates that member countries remain bound by their obligations for a period of one year after notifying their withdrawal.
Burkina Faso, Mali and Niger were founding members of ECOWAS in 1975
Burkina Faso, Mali and Niger were founding members of ECOWAS in 1975, but the bloc suspended all three and imposed sanctions on them following military coups that overthrew elected civilian governments.
Withdrawal will hit hard given that ECOWAS guarantees visa-free travel and right of settlement and work in member countries. Losing such benefits will cause concern, as will the potential effect on regional trade.
The leaders of the three Sahel nations issued a statement saying it was a "sovereign decision" to leave the Economic Community of West African States "without delay".
It is the latest move by Burkina's military rulers to strengthen ties with Moscow, as the country looks to diversify its international allies following a coup last year.