Rahmatullah Rahmat, the Paktia governor, said the bomber struck as a convoy of foreign forces was passing through a street market in the city of Gardez.
A spokesman for the International Security Assistance Force, which leads thousands of foreign troops in the country, said there were casualties among its forces at the scene but no deaths.
The attack in Kunduz on Saturday was aimed at German soldiers who were shopping in a crowded market. The Taliban claimed responsibility.
The Taliban has vowed to step up suicide attacks across the country to avenge the killing of Mullah Dadullah, its top military commander, last week.