A senior Indian embassy diplomat said that the bomb targeted the Indian embassy.
"It was a suicide car bomb attack. There are civilian and police casualties," Zemarai Bashary, an Afghan interior ministry spokesman, said.
One report said that two cars, one marked with UN insignia, were badly damaged in the blast.
Smoke was seen rising from downtown Kabul and the windows of shops in the blast area were smashed.
Shortly after the blast, Taliban claimed responsibility for the attack in its official website and identified the attacker as Khalid.
Zeina Khodr, Al Jazeera's correspondent in Kabul, said: "Intelligence officials are telling us the target was the Indian embassy.
"A suicide car bombing right outside the embassy, the car was parked outside. They say that there are scores of casualties.
"Afghan government and intelligence sources have made clear to Al Jazeera that they believe that foreign hands were involved. This was an operation which was planned by a state and not - I quote - a group of bandits."
Vishnu Prakash, an Indian foreign ministry spokesman, said in New Delhi: "As per reports we have received all embassy personnel are safe. There has been some damage to the embassy property.
"We are closely monitoring the situation."
The Afghan interior ministry is on the opposite side of the road from the Indian embassy.
Kabul has been hit on multiple occasions recently by suicide bombings and roadside bombs.
Dozens of people were killed in an attack on the Indian embassy in July 2008, since which time the access road has been barricaded.
Two senior Indian diplomats were among the 58 people killed in the 2008 attack.