Ahmad Shah Waheed, deputy minister for public works, was taken by gunmen at around 7:00 am (0230 GMT) from the Khairkhana neighbourhood of the capital, said the official who declined to be named.
He did not elaborate, saying more information could harm efforts to recover the men.
Hashmatullah Stanikzai, Kabul police spokesman, confirmed the incident, adding: "Afghan police forces have launched a search to secure his release."
The motive for the incident is not clear, but kidnapping of wealthy individuals for ransom is common in Afghanistan.
The abduction comes as officials count votes from the April 5 election to choose a successor to President Hamid Karzai.
Early results suggest former foreign minister Abdullah Abdullah, runner up in the 2009 presidential poll, is leading his closest rival Ashraf Ghani, but a run-off is likely.
Whoever emerges victorious facings a testing time as Afghanistan takes on the still-resilient Taliban insurgency without the support of NATO combat troops, who are pulling out this year.
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