He said 36 people were wounded in the attack and three of them were in a critical condition.
A parked car packed with explosives was detonated by remote control as the police bus drove by, Reuters cited CNN Turk as saying.
CNN broadcast cell-phone footage of a blackened and mangled vehicle on the street as vendors peered out from a souvenir shop in a district near Istanbul University.
There was no immediate claim of responsibility. But Kurdish militants, Daesh (ISIL) and radical leftists have all staged attacks in Turkey recently.
A witness saw what appeared to be two police vehicles hit, one of them on its side next to the road. Gunshots were heard in the area after the blast.
Broadcasters showed armed police in the street near the site where the blast struck. Media reports said eight people were wounded.
A spokesman at police headquarters in Istanbul was unable to provide information on the incident when reached by phone.
Turkey has suffered a spate of bombings this year, including two suicide attacks in tourist areas of Istanbul blamed on Daesh and two car bombings in the capital, Ankara, which were claimed by a Kurdish militant group.