Interior Minister Suleyman Soylu said a moving car was detonated targeting riot police on duty near a stadium in the district of Besiktas, where a football match ended about one and a half hour before, Xinhua news agency reported.
Deputy Prime Minister Numan Kurtulmus said the blast occurred soon after the fans left the stadium.
A minute later, a man blew himself up in Macka Park just across the stadium, Soylu said.
At least 10 suspects were detained in connection with the blasts while six prosecutors tasked with investigating the attacks.
Three of the injured were in critical condition, said Health Minister Recep Akdag.
Turkish President Recep Tayyip Erdogan vowed to “continue our struggle” despite more bloodshed.
No group has claimed responsibility of the attacks but a series of bombings in the country this year has been carried out by Islamic State terrorists.