Two militants on motorbikes seized the father of Education Minister Farouq Wardak in Wardak province's Sayed Abad district on Monday, said provincial Governor Halim Fedai.
The minister's family is in contact with the kidnappers, said Sher Wali Wardak, another son of the kidnapped 80-year-old Khoja Mir.
Kidnappings of wealthy Afghans have spiked over the last year, often carried out by criminals and militants seeking money or political leverage.
In eastern Afghanistan, meanwhile, a U.S. Air Force Predator drone crashed Tuesday, U.S. Central Command said in a statement.
"The crash was not due to hostile fire," the statement said. It did not give a reason for the crash.
In southern Uruzgan province, police clashed with militants in Khas Uruzgan district, killing seven suspected insurgents Tuesday, said Juma Gul Himat, the provincial police chief. Two policemen were wounded in the clash.
Southern Afghanistan is the center of the Taliban-led insurgency, which has made a violent comeback the last three years. President Barack Obama has ordered 21,000 new U.S. troops to Afghanistan this summer to try to reverse the militants' gains. The U.S. has some 38,000 troops in the country today, approximately half of the 70,000 international forces in Afghanistan.