The Dogan news agency said the clash, which also left four police lightly wounded, took place in the Gaziosmanpasa district in the north of the European side of the city.
The report did not specify which organisation the two suspects were affiliated with.
But Gaziosmanpasa is known as a stronghold for supporters of the outlawed Kurdistan Workers' Party (PKK) and the ultra-left Revolutionary People's Liberation Party-Front (DHKP-C).
The report said the pair were part of a cell linked to a mysterious bomb attack on December 1 near an Istanbul metro station that wounded up to half a dozen people.
Today's clash, which lasted half an hour, took place when militants opened fire on the police carrying out the raid, who responded, Dogan said.
Turkey is on alert after 103 people were killed on October 10 when two suicide bombers ripped through a crowd of peace activists in the capital Ankara, the worst attack in modern Turkey's history.
Turkish authorities have in recent weeks detained several suspected members of the Islamic State (IS) group with officials saying they were planning attacks in Istanbul.
But Turkey is also waging an all-out assault on the PKK which has staged dozens of deadly attacks against members of the security forces in the southeast of the country.
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