The attack occurred about 3:30 p.m., targeting a bus carrying police from a training center on Kabul's busy Pul-e-Charki road, said Kabul police spokesman Hashmat Stanikzai.
The force of the blast was so great the bus was blown off the ground and crashed 10 yards away, witnesses said. Pieces of twisted wreckage littered the road.
More than 100 police and intelligence forces -- as well as French soldiers from the NATO coalition -- responded to the scene.
A spokesman for the Taliban claimed responsibility for the attack, which again demonstrated the insurgents' ability to strike in the heart of the capital even as Afghanistan prepares for presidential elections in April and U.S.-led coalition forces plan to withdraw by the end of 2014.
Hamed, a 22-year-old construction company owner who witnessed the explosion, said the blast was huge and rushed to the scene.
"I saw more than 20 wounded," said Hamed, who like many Afghans goes by one name. "My uncle and I carried about 12 wounded police and civilians in our own cars to the hospital."
Baktash is a Times special corespondent.