General Alishah Paktiawal, the Kabul criminal investigation police chief, said the bomber struck a few hundred metres from the parliament building.
"It was a suicide bombing. Four people were killed and four others were injured. The bomber was driving a yellow and white taxi," Paktiawal said.
He said it was unclear if the bomber was targeting the parliament building. "An investigation is under way," he said.
Iraq-style suicide attacks are common in southern Afghanistan, where the insurgency is at its strongest, but rare in Kabul.
Four civilians were killed and another 12 wounded when a suicide bomber targeted an intelligence director's vehicle in Kabul on March 28. The intelligence official survived.
About a week earlier a suicide attacker rammed an explosives-filled car into a US embassy convoy in the capital, wounding five embassy staff and guards and at least three passers-by.
In the deadliest attack in Afghanistan this year, more than 20 people including two Americans and a South Korean soldier were killed on February 27 in an attack on the main US base at Bagram, about 60km from Kabul, while Dick Cheney, the US vice president, was visiting.
The Taliban has vowed a wave of such blasts this year after nearly 140 last year across the country killed about 200 civilians and scores of Afghan and foreign security officials.