The explosions, believed to be a car bomb and a suicide bomb, targeted police officers, officials say.
Witnesses heard gunfire after the attack, which came two hours after fans had left the Besiktas stadium.
Ten arrests were made. Turkey has seen a recent spate of deadly militant attacks in major cities.
No group has said it was behind the attack but a wave of bombings in Turkey this year has been carried out by Kurdish militants and so-called Islamic State (IS), the BBC’s Turkey correspondent, Mark Lowen, reports.