The blast, in the Beyazit neighborhood of Istanbul's historic Fatih district, occurred about 8.40 a.m. local time during morning rush hour.
It killed seven police officers and four civilians, and left 36 people injured, three of them critically, Istanbul Gov. Vasip Sahin told reporters.
Local media reported that the blast was remotely detonated as the bus, carrying a group of riot police, passed. No group has taken responsibility for the bombing.
The area surrounding the explosion -- a busy neighborhood that includes the city's landmark Beyazit Square, the main Istanbul University campus and the Vezneciler metro station -- was evacuated following the blast.
Images from the site of the explosion showed visible damage to surrounding buildings, with windows blown out and glass strewn across the street.
Erdogan calls attack unforgivable
Turkish President Recep Tayyip Erdogan, who visited some of the wounded in the hospital, offered his condolences and said the attack was unforgivable.
Turkish President Recep Tayyip Erdogan visits a man injured in the blast.
"Let me be clear, terrorist organizations distinguishing between civilians, soldiers and police does not mean anything to us. The end target is always human beings," he said.
"The mission of our soldiers, our police and our city guards is to protect our lives and our property. It is unacceptable that these people are targeted. We will continue our fight against terrorism fearlessly," he said.
He told reporters that those responsible had "once again shown that they are the enemy of human values," Turkey's Anadolu state news agency reported.
The United States, France and Germany were quick to condemn the attack, with French President Francois Hollande saying in a statement that "this intolerable act of violence must more than ever confirm our mutual determination to fight all forms of terrorism."
The U.S. Embassy in Turkey said on Twitter that it would "continue to stand shoulder-to-shoulder with Turkey in the fight against terrorism."
Wave of attacks
Turkey has been rocked by a string of terror attacks over the past year as it weathers bombing campaigns carried out both by ISIS and Kurdish militants.
As part of the U.S.-led coalition against ISIS, Turkey allows coalition planes to fly raids on ISIS targets in neighboring Iraq and Syria from its territory.
And last year Turkey resumed hostilities with Kurdish militant separatists the PKK in earnest after a two-year cease-fire broke down.
The PKK, or Kurdistan Worker's Party, has been in an armed struggle with the Turkish government for decades and is considered a terror group by Turkey, the United States and the European Union.
Six days later an ISIS suicide bomber detonated himself on one of Istanbul's main streets, killing four.
The violence has had an impact on Turkey's tourism industry, a key sector of the national economy.
CNN's Stephanie Halasz contributed to this report.
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