The two bombs exploded less than a minute apart on Saturday night, in a coordinated attack on police shortly after a soccer match between two of Turkey's top teams.
Turkish officials said the blasts, believed to be a car bomb and a suicide bomb, had targeted police officers.
Interior Minister Suleyman Soylu said: "It is thought to be a car bomb at a point where our special forces police were located, right after the match at the exit where Bursaspor fans exited, after the fans had left.
No group has said it was behind the attack but a series of bombings in the country this year has been carried out by Islamic State (IS) terrorists.
President Recep Tayyip Erdogan confirmed fatalities but gave no details.
"A terrorist attack has been carried out against our security forces and our citizens," he said.
"It has been understood that the explosions after the Besiktas-Bursaspor football game aimed to maximise casualties. As a result of these attacks unfortunately we have martyrs and wounded."
Turkey has seen a recent spate of militant attacks in major cities that have left dozens of people dead.