Sayed Fazalullah Wahidi was here with his family to get a visa for the UK.
A police official said the governor was staying in a guest house in the capital and went with his grandson to a nearby market when he was kidnapped. The kidnappers left the child and took Wahidi away.
"A search has been launched to recover the former governor," the official said.
A case has been registered at Kohsar Police Station located in the Jinnah Supper Market area on behalf of the family and the Afghan embassy.
Wahidi was close to former president Hamid Karzai and his disappearance could sour ties between Pakistan and Afghanistan ahead of the planned start of talks between the Taliban and Afghan officials by the end of the month.