"It's a tragedy," police Commissioner Charles Ramsey said.
The incident in Feltonville, a neighborhood of row houses in North Philadelphia, began with two men stealing a motorcycle at gunpoint, Ramsey said. One man fled on the motorcycle, and the other sped away in a car, he said.
Police spotted the car a few minutes after receiving a report of the motorcycle theft and pursued it for about a mile.
The car jumped the curb with such force it badly damaged the concrete steps of one of the row houses, where the children lived. It became wedged between a house and a pole. The woman it hit is the mother of at least one of the dead children, all of whom were under age 10, authorities said.
"It's horrifying to think about what happened," Mayor Michael Nutter said at the scene. "It's a horrific scene."
The car's driver was injured and was arrested at the scene, and a gun was found in the car, police said. The motorcycle rider was arrested at his nearby home, where several weapons were found, police said.
Officers were attacked by a dog at the motorcycle rider's home and had to shoot it but didn't kill it, said police, who recovered two shotguns, two handguns and a rifle there.
Police towed away the mangled car, whose back passenger side and roof were caved in. They didn't immediately release the names of the victims or those arrested.
Neighborhood resident Robert Martinez, who lives in the house directly behind the crash scene, said the sound of the crash "was like a bomb blew up."
Martinez, who knew the victims, said he hustled to the scene and heard the children's grandmother, who lived with them, calling out for them.
"It could have been my three nieces," he said, "could have happened on this block."