According to a written statement by the Security Directorate of Erbil city, where the attack took place, the alleged attacker Mazlum Dag, who was identified two days ago, has been detained by security forces.
The Turkish vice consul to Iraq's autonomous Kurdish region was shot dead Wednesday in the local capital Arbil.
No group has claimed responsibility for the attack, but Ankara on Thursday launched a "comprehensive air operation" against the PKK in Iraqi Kurdistan's Qandil mountain area.
The Department of Foreign Affairs (DFA) on Friday urged the Filipino community in Iraq to be vigilant following a terrorist attack that killed 3 people, including a Turkish diplomat.
The statement did not give further details, but said the suspect was already wanted by security agencies in Iraq's Kurdish region.
It said it strongly condemned the attack on the diplomat, and said "using the attack as a reason to make one of our lawmakers a target through the name of her brother is a provocation and unacceptable".
Iraq's self-governing Kurdish region is politically allied with the Turkish government, but PKK militants, who have fought a decades-long insurgency against Ankara, operate in parts of the territory.
The HDP, the country's second largest opposition group, is regularly accused by President Recep Tayyip Erdogan of links to Turkey's outlawed separatist Kurdistan Workers' Party (PKK).