The clashes -- the most serious yet between the Turkish army and IS -- came after the killing of 32 people in a suicide bombing Monday, blamed on IS, sparked an upsurge in violence.
A day after the fatal shooting of two police claimed by Kurdish militants as "revenge" for the suicide bombing in the town of Suruc on the Syrian border, a policeman was shot dead in the majority Kurdish city of Diyarbakir.
The Dogan news agency said four soldiers had been wounded.
Turkish tanks from the fifth armoured brigade then responded by opening fire on targets controlled by IS jihadists in Syria, NTV television said, adding that one IS militant had also been killed.
Thirty-two people -- mainly young activists, one as young as 18, preparing for an aid mission to Syria -- were killed on Monday in a devastating suicide bombing in Suruc.
That attack marked the first time the government had explicitly blamed IS for a strike in the country.
Turkey has been accused of colluding in the past with IS extremists in the hope they might prove useful in its aim of knocking out Syrian President Bashar al-Assad. Ankara has always vehemently denied the claims.
The military wing of the Kurdistan Workers' Party (PKK) claimed the killing of the two police in the border town of Ceylanpinar, accusing the two slain officers of collaborating with IS extremists.
Aged 24 and 25, they were given a funeral ceremony with full honours outside police headquarters in the regional centre of Sanliurfa, their coffins draped in the Turkish flag.
The state Anatolia news agency said the three suspects had been arrested in early morning raids and were being questioned, without giving further details.
In the latest violence one Turkish policeman was shot dead and another badly wounded in an attack Thursday by armed men during a routine traffic check in Turkey's majority Kurdish-city of Diyarbakir, hospital sources said.
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