Police Chief Huseyin Capkin said the bomb was not a powerful one, but was still designed to cause "moderate" destruction. Police were investigating whether the target was a police training school nearby.
"Our consolation is that no one was killed," he said.
Capkin said one of the injured was a policeman who was passing by. He said none of the injured was in life-threatening condition. The Dogan news agency reported, however, that one woman had lost a leg in the blast.
CNN-Turk television said the explosion occurred as a bus passed by, shattering its rear windows and injuring passengers in the back of the vehicle.
Five vehicles in total were damaged in the blast, Capkin said. Fearing a secondary blast, police sealed off the area with yellow tape and bomb disposal experts arrived. Investigators prepared to search for clues.
There was no immediate claim of responsibility and the police chief refused to say who may be behind the attack.
Kurdish rebels are fighting for autonomy in southeastern Turkey and have carried out bomb attacks in Istanbul in the past. Their jailed leader has warned of more violence if their demands for negotiations are not met after elections on June 12.
Turkey also has a history of attacks by Islamic and leftist extremists.
"They will not get away with it," Capkin said of the culprits. "The people of Istanbul should feel at ease."