A gunman opened fire at a restaurant in Erbil where Turkish diplomats were dining before fleeing in a car driven by an accomplice, two Kurdish security officials and a witness said.
US Secretary of State Mike Pompeo strongly condemned the murder of the Turkish diplomat.
"There can be no justification for such acts of wanton violence," Pompeo said in a statement.
"The US reaffirms its commitment to support the government and people of Turkey and Iraq," he added, extending his condolences to the families of the victims, AFP reported.
There was no immediate claim of responsibility as security forces began a search for the attackers.
Turkey, Iraq's central government in Baghdad and Kurdish authorities in Erbil condemned the attack, which took place weeks after Turkey launched a new military offensive against Kurdish separatist militants based in northern Iraq.
Ankara's main enemy in Iraq is the PKK group, which has based fighters in the mountainous border region, north of Erbil, during its decades-long insurgency in southeastern Turkey.
Turkey and the ruling Kurdish party in Erbil, the KDP, have blamed the PKK for other Turkey-related incidents in northern Iraq including the storming of a Turkish military camp earlier this year.
Turkey's foreign ministry said one of those killed was a diplomat working at its consulate to semi-autonomous Iraqi Kurdistan.
Turkey Presidential spokesman Ibrahim Kalin vowed on Twitter: "The necessary response will be given to those who committed this treacherous attack".
A statement from the Kurdish internal security service said two people were killed - the diplomat and another civilian - and one other person was wounded.
One witness said an attacker entered the restaurant and started shooting before he fled in a car that was waiting for him outside.
It was a rare major security incident in Erbil, where a new president and prime minister, part of a clan that has controlled the KDP for decades, recently took office. The KDP has said it will continue to co-operate closely with Ankara against the PKK.
"Nobody invited them (the PKK) here," Prime Minister Masrour Barzani said in an interview with Reuters this month.
"We disapprove of their activities and ... of their presence here. We understand the concerns of the neighbouring countries about security issues," he said, adding that Erbil would look to strengthen relations with Turkey.
Turkey has called for Baghdad to take a more active role in helping it eliminate the PKK, and has waged offensives in recent years against PKK allies in northern Syria.
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