World Bulletin / News Desk
Mohamed Bazzoum said on Twitter that the attack started around 4 a.m. [0300GMT] and lasted a few hours before being repelled by security operatives.
"The enemy was repulsed, leaving many [attackers] wearing explosive belts dead," Bazzoum added.
He did not say if the jailbreak succeeded.
Some top Boko Haram commanders and other extremists from across the Lake Chad region are being held in the prison, a military source said, adding the jailbreak might be an attempt by their comrades to free them. The source wished to remain anonymous due to restrictions on speaking to the media.
Koutoukale is situated some 50 km (30 miles) away from the capital, Niamey.
Like Nigeria, Cameroon and Chad, Niger has had a bitter taste of the Boko Haram insurgency which has claimed lives of tens of thousands of civilians and servicemen alike. Millions of people have also been displaced across the region.
Niger's Diffa region has suffered several deadly attacks by Boko Haram. In July, 38 civilians, including 10 children, were massacred in villages near Diffa.
Niger is part of a military coalition with Chad, Benin, Cameroon and Nigeria to combat Boko Haram.