The Ministry of Interior (MoI) said the detained Taliban leader has been identified as Abdullah and was held from the vicinity of Khanabad district.
MoI further added the operation was conducted by Public Order Police forces on Sunday.
Another senior Taliban leader identified as Abdul Wakil was also arrested during the same operation, MoI said, adding that an automatic rifle was confiscated from the detained militants.
The anti-government armed militant groups including the Taliban insurgents have not commented regarding the report so far.
Kunduz is among the relatively volatile provinces in northern Afghanistan where the Taliban insurgents are actively operating in a number of its remote districts.
A group of Taliban insurgents suffered casualties in a premature bomb explosion in this province earlier this week.
According to the local security officials, the incident took place late on Saturday night in Imam Sahib district.
A spokesman for the 20th Pamir Division, Gen. Ghulam Hazrat Karimi, said one militant was killed as he was planting an Improvised Explosive Device (IED) in Qerghiz area.