Katsina is among states in northwestern and north central Nigeria where armed gangs on motorbikes have killed people or kidnapped them for ransom from villages and highways.
Police spokesman for Katsina Gambo Isah confirmed the abduction of the children. He did not give further details.
Police records showed that at least 22 children were missing.
Residents told Reuters that the children were taken on Sunday while harvesting crops at a farm located between Kamfanin Mailafiya and Kurmin Doka villages in Katsina.
A resident whose son was among those kidnapped said 30 children were abducted but that at least two escaped while another one was released because she was sick.
"Only four of the children are boys, the rest are girls aged below fourteen (years)," said the resident, who declined to be named for safety reasons.
A village head from the area said the gunmen were demanding 30 million naira ($68,435) as ransom.
The military has been bombing suspected bandit hideouts as concerns rise ahead of a general election next February to choose Buhari's successor.