The bomb was hidden outside the home of a former commander, deputy police chief Abdul Hakim Hungar said on Monday.
The former commander, Agha Shah, was allied to the US-backed Northern Alliance and assisted in the US-led invasion of Afghanistan.
The blast killed the former commander, a supporter of President Hamid Karzai, as well as three other civilian passers-by, he said. The three injured were taken to hospital.
He said it was not immediately clear who was responsible for the blast.
The bombing came a day after an explosion in the city injured four British government officials.
Attacks against Karzai's US-backed government, its supporters, and international military forces have increased, leaving more than 1300 dead in the past six months.
US soldier killed
Meanwhile, in eastern Afghanistan, a US soldier was killed and another was wounded, the US military said on Monday.
American and Afghan troops were carrying out a military offensive operation in eastern Paktika province on Friday when they came under fire, a military statement said.
The wounded soldier was evacuated to a nearby base and was in stable condition, it said.
"This is a sad and tragic moment for us all," said Brigadier-General Jack Sterling, a deputy commander of the US-led coalition. "The soldiers serving here in Afghanistan are fighting on the very edge of freedom's blade, and the loss of anyone is a deep and painful event."
The identity of the soldiers was not released pending notification of next of kin.
The death beings to 201 the number of US troops killed in the region since US-led forces invaded Afghanistan in late 2001.