The rescue took place on Saturday, with air force personnel raiding a site at Pauwa Hill, in the Kankara local government area, Katsina state internal security commissioner Nasir Mu'azu said in a statement.
The operation was staged following an air force strike in the hunt for a "notorious bandit kingpin" and his gang suspected to be behind an attack Tuesday on a mosque and on nearby villages that claimed 50 lives, said the statement.
Mu'azu said that the operation "successfully" rescued 76 kidnapped people, including women and children.
"However, it was regrettably noted that one child tragically lost his life during the ordeal," he said.
There was no information on the number of casualties among "bandits", as members of criminal gangs are locally known.
In some past cases, families of victims have disputed official claims of rescue and reported having to pay ransoms for the release of captives.
Mass kidnappings for ransom are common in Nigeria's northwest and central states, where heavily armed gangs often target remote villages to loot and abduct residents.
The gangs have turned cattle theft, kidnapping and imposing taxes on farmers into huge moneymakers across the impoverished countryside, where the government's presence has long been nearly non-existent.
Nigeria's banditry crisis originated in conflicts over land and water rights between herders and farmers, which has since morphed into organised crime.
The militias have no ideological leaning and are motivated by financial gain, but officials and analysts have expressed concern over growing pragmatic alliances with jihadists from Nigeria's northeast.
