Twenty-seven of those killed were police and two were civilians, he told reporters in Istanbul, adding that 10 suspects had already been detained over the bombing.
Soylu said the first blast was caused by a car bomb that struck outside Besiktas's football stadium.
It was followed 45 seconds later by another attack at nearby Macka Park, carried out by a suicide bomber who blew himself up in the midst of police officers.
The minister said the government suspects the two bombings were linked.
The authorities did not say who was behind the blasts but the attacks were the latest in a year that has seen Istanbul and other Turkish cities rocked by a string of attacks blamed on Islamic State jihadists and Kurdish militants.