Two other assailants were wounded and captured during Tuesday's shootout in the city's financial and business district while two police officers sustained slight injuries, officials said.
Israel had withdrawn its diplomats from Turkey over security concerns and deteriorating relations with the country's officials shortly after the start of the war in the Gaza Strip, and officials said the consulate was closed at the time of the attack.
Interior Minister Mustafa Ciftci said one of the assailants had links to a group that he said "exploits religion," without naming the organisation.
The Islamic State group has carried out deadly attacks in Turkey in the past.
Anadolu Agency reported that security forces detained nine suspects in operations conducted in Istanbul as well as in the provinces of Konya and Kocaeli.
They were being questioned along with the two injured assailants, the agency reported, without providing further details.
Cifti said the attackers had travelled from the city of Izmit, in Kocaeli province, in a rented car.
The two wounded assailants are brothers, identified as Onur C and Enes C.
The first has a criminal record related to drugs.
Israel's foreign ministry on Tuesday condemned the attack and praised the Turkish authorities for preventing further violence.
