Falling debris damaged a house in the Kirkuk city centre, police and army officials told AFP, speaking on condition of anonymity.
Iraqi security forces said they were investigating the "circumstances of the incident".
There were no reports of any direct casualties but the police official said a carpenter working on a nearby building site had been admitted to hospital after a fall.
"A Turkish drone which penetrated Iraqi airspace has been shot down," the deputy air defence commander for Kirkuk, General Abdel Salam Ramadan, told a press conference at the site of the downing.
The aircraft had come "from the direction of Sulaimaniyah", the autonomous Kurdistan region's second city to the north, Ramadan said.
In a statement published several hours later, the Joint Operations Command of Iraqi forces confirmed that the drone was Turkish and was detected by Iraqi air defences.
However, it said an investigative committee would "determine the reasons for the (drone's) fall" and the "circumstances of the incident".
On social media site X, Turkish foreign ministry spokesperson Oncu Keceli said: "Coordination has been ensured with the Iraqi authorities to clarify the incident in all details."
Keceli added that "Turkey is fully determined in the fight against terrorism", a reference to the Kurdistan Workers' Party (PKK).
Ethnically mixed Kirkuk and its surrounding oil fields do not form part of Iraq's autonomous Kurdistan region and are directly administered by the federal government in Baghdad.
Turkey has maintained dozens of military bases in northern Iraq for the past quarter of a century as part of its campaign against militants of the PKK.
Its troops routinely carry out operations against PKK targets but it comments on them only sporadically.
The Iraqi federal government discreetly outlawed the PKK as a "banned organisation" in March and earlier this month agreed a military cooperation deal with Ankara that will see joint training and command centres set up in the fight against the militants.
The leftist group, which has waged a deadly on-off insurgency against the Turkish state since 1984, is blacklisted as a "terrorist organisation" by Ankara and its Western allies.
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