Two police chiefs were among the deceased and at least 166 people were injured, Suleyman Soylu told reporters in Istanbul.
Ten suspects have been detained as part of an ongoing probe, he added.
Health Minister Recep Akdag said 20 of the injured have been discharged from hospital while 17 are in surgery, and six are in intensive care units, three of them in critical condition.
Two blasts rocked the city, a car bomb followed within the minute by a suicide bomb, Deputy Prime Minister Numan Kurtulmus explained.
Turkish Prime Ministry said in a statement, a day of national mourning has been declared on Sunday.
President Recep Tayyip Erdogan said the attack targeted police and civilians alike, and sought to cause the most casualties.
"When Turkey takes a positive step towards the future, the response comes immediately in the form of blood, loss of life, brutality, and chaos by terrorist organizations," Erdogan said.
Prime Minister Binali Yildirim earlier said the government would dedicate every resource possible to thoroughly investigate the "vile attack”.
"The murderers who ambush life, peace, and happiness will not defeat the integrity of the state and the nation. They will not be able to divert Turkey from the path of democracy and law," Yildirim said.
The explosion occurred two hours after a Turkish football league match between Besiktas and Bursaspor at the Vodafone Arena.
AA/MNA