Hijratullah Akbari, a spokesman for Kunduz police chief said the attack was on Wednesday evening.
Mullah Khairullah, along with four of his men were killed in the operation, he added.
Akbari further added, Khairullah has worked as the Taliban military commander for several years.
Based on the source, a citizen of Pakistan was also among those killed.
The Taliban group did not comment on the report so far.