Tuesday’s bomb explosion targeted prominent Afghan lawmaker Mohammad Mohaqiq, police said.
The member of parliament escaped unhurt.
"Three civilians were killed and 24 others, including some guards, are wounded," AFP quoted Mohammad Zahir, the CID chief of Kabul as saying.
Mohaqiq is the founder and chairman of the People's Islamic Unity Party of Afghanistan.
The incident took place the same day Afghan security forces took
over the security responsibility for the last remaining areas of the
country from the US-led foreign troops.
Afghan President Hamid Karzai said Tuesday that Afghan security forces would be in charge of security for the entire country.
"Our security and defence forces will now be in the lead," he said in a speech. "From here, all security responsibility and all security leadership will be taken by our brave forces."
US-led NATO countries have previously announced that they will partially withdraw their troops from Afghanistan in 2014.
However, the partial pullout contradicts a recent agreement that calls for the full departure of foreign forces from Afghanistan by the end of next year.
According to the latest figures released by the website icasualties.org, 3,335 foreign soldiers have been killed in Afghanistan since the US-led war began in October 2001.
The US-led war in Afghanistan removed the Taliban from power, but insecurity continues to rise across the country, despite the presence of thousands of US-led troops.