Asadullah Kakar, a provincial council member in southern Zabul province, says that the exchange took place in Jaghori district of Ghazni province today.
Kakar says that the exchanged 22 people, including women and children, probably are family members of the kidnappers.
He says the kidnappers asked for another six more people in exchange for the remaining 11 Hazara hostages they hold.
It wasn't immediately clear how the Uzbeks came into government custody.
The Hazara are a Shiite ethnic group in Afghanistan.