Eleven of the dead were civilians and one was an Afghan police officer, the Interior Ministry said in a statement.
At least 84 people, including members of Afghan security forces, were wounded in the attack, which struck a shop-lined road between the Indian Embassy and the Interior Ministry, said Health Ministry spokesman Ahmad Farid Raaid.
The blast hit shortly after 8:30 am, just as residents were arriving for work. It shattered glass and rattled buildings more than a kilometre away. A huge brown plume of smoke was visible in the air as ambulances raced to the scene and carried away the wounded.
One 21-year-old man named Najibullah said he had just opened his shop when the explosion went off, knocking him unconscious.
When he awoke, he said, he couldn't see anything.
"Dust was everywhere. People were shouting," said Najibullah, who like many Afghans uses only one name. "You couldn't see their faces because there was so much dust."
His white clothes were covered in blood after helping load four injured onto ambulances.
In New Delhi, India's Foreign Secretary Nirupama Rao said the Indian Embassy was the target.
"I believe the suicide bomb was directed at the embassy since the suicide bomber came up to the outer perimeter wall of the embassy in a car loaded with explosives," Rao told reporters.
Three Indian paramilitary soldiers on guard duty at the embassy's watchtower were wounded by shrapnel, Rao said.
She said the intensity of the blast was similar to the one that occurred outside the building on July 7, 2008, that killed dozens of civilians. The road in front of the embassy has been barricaded since then. The Afghan Interior Ministry is just across the street Indian Embassy.
The explosion hit a day after the Afghanistan war reached its eighth anniversary and as President Barack Obama considered a request for between 10,000 and 40,000 additional troops prepared by the top US commander in Afghanistan, Gen. Stanley A. McChrystal.
The Afghan capital has been hit numerous times by suicide bombers and roadside bombs, several since the run-up to the country's disputed August 20 election. The attacks usually target international military forces or government installations, but Afghan businesses and civilians are also often killed or injured.
In the most recent attack in mid-September, a suicide car bomber rammed into an Italian military convoy on a road leading to the airport. That blast killed six Italian soldiers and 10 Afghan civilians.
Interior Ministry spokesman Zemeri Bashary said Thursday's explosion was also a suicide car bomb, but he had no details and there was no immediate claim of responsibility.
The Indian news channel CNN-IBN cited Jayant Prasad, Indian ambassador in Kabul, as saying there has been "extensive damage to the chancery." He said that the vehicle-borne bomb was so powerful that it blew off the some the embassy's doors and windows.
President Hamid Karzai's office condemned the attack.
AP Television News footage from Kabul on Thursday showed local residents and soldiers pulling a charred, severed leg out of a destroyed vehicle. Others carried an apparently lifeless body on a stretcher to an ambulance.
On another stretcher, a man lay face down, one arm hanging downward, his back left leg covered in blood.
Two sport utility vehicles nearby were badly damaged, according to an Associated Press reporter at the scene. One of them had UN markings on its side.
UN spokesman Dan McNorton confirmed two of the world body's vehicles were near the blast and one was damaged. Both vehicles had only a driver inside, and neither was wounded. The United Nations typically uses armored vehicles in Kabul that are designed to withstand such attacks.
The blast could be heard miles (kilometers) away. Windows in dozens of surrounding shops at the scene of the blast were shattered, and walls of buildings were badly damaged in the blast, though none of the multistory buildings along the commercial thoroughfare had collapsed.
One injured man said the force of the explosion threw him into the air. Mohammad Arif said he was leaving the Indian Embassy when the blast tossed him against a concrete barrier. The left side of his head was bleeding as he spoke.
