The explosives were remotely detonated as the vehicle passed through the busy Vezneciler district at the morning rush hour, reports said.
Four civilians and seven police officers were among the dead, Istanbul’s governor, Vasip Sahin, said. Some 36 other people were injured, he added.
No group has said it carried out the attack.
Turkey violence has escalated recently as a result of tensions with Kurdish separatists and the conflict in neighboring Syria.
The explosion happened near the city’s historic Beyazit Square neighborhood, a major tourist attraction.
Pictures showed the wreckage of a bus destroyed and the facade of nearby buildings damaged. Armed police were also seen next to the site.
Reports said gunfire was heard in the area after the blast.
ISIS and Kurdish militants have both carried out bloody attacks in Turkey in recent months.
President Recep Tayyip Erdogan has said terror groups are targeting civilians because they are losing their struggle against Turkish security forces.
Turkey is part of the US-led coalition against ISIS and allows coalition planes to use its air base at Incirlik for raids on Iraq and Syria.
A two-year-old ceasefire between Turkey and the Kurdish militant PKK broke down last summer.
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