The defence ministry said "commandos" moved in, supported by drones and helicopters, following a bombardment with rocket launchers and artillery guns that hit more than 150 targets.
It said the operation, dubbed "Claw-Tiger", came after a "recent upsurge in attacks on our police stations and military bases" near the Iraqi border.
Turkey carried out air strikes earlier this week that drew an angry response from Iraq, which labelled them "a violation of sovereignty".
The Turkish military regularly carries out operations against the Kurdistan Workers' Party (PKK) in southeast Turkey and its rear bases across the border.
The operation on Sunday night was dubbed "Claw-Eagle" with raids in the northern Iraqi territories of Kandil, Sinjar and Hakurk.
A PKK source in northern Iraq told AFP Turkish forces "carried out a commandos airdrop from military helicopters backed by warplanes, and clashed with our fighters" in an area called Haftanin, which is in Dohuk province near the Iraqi-Turkish border.
Reda Manujri, an independent analyst in northern Iraq, said Turkish troops would likely seek to occupy a "strategic mountain chain" along the border between Iraq and Turkey, possibly even setting up military bases there.
The expert said the "silence" from the Kurdish regional government and Baghdad "indicates that they both had information from, an understanding with, and perhaps even collusion with the Turkish government on this attack".
PKK bases are not explicitly authorised but are tolerated by an autonomous Kurdish administration in northern Iraq.
President Recep Tayyip Erdogan’s ruling party spokesman defended Turkey’s actions.
"Turkey continues its effective fight against terror using its rights based on international law,” Omer Celik said on Twitter.
"It is our most natural right and duty to fight against terrorists who attack our borders, citizens and security forces.”
The PKK, which has fought an insurgency against the Turkish state since 1984, is banned as a terrorist group by Ankara and its Western allies.
Tens of thousands have been killed during the violence, which resumed after a two-year ceasefire collapsed in 2015.
Iraq summoned Turkey’s Baghdad Envoy Fatih Yildiz over the raids on Sunday night.
The ambassador tweeted he had informed Iraqi officials that Turkey would "fight the PKK wherever it is” if Iraq did not "take any steps” to remove the PKK’s presence.