The Kurdistan Region Security Council published a picture of the suspect Saturday, saying he was arrested by security and counterterrorism units following a large-scale operation.
Mazlum Dag has two other brothers, both of whom are wanted by Turkish authorities for being members of PKK.
It later announced it had also arrested Mohammad Biskesiz, identifying him as "one of the accomplices of Mazloum Dag".
Turkey's state-run Anadolu Agency claimed that two of the suspect's siblings were alleged PKK militants and that a third was a legislator from Turkey's pro-Kurdish party. The PKK has been designated a "terrorist" group by Ankara, the European Union and United States.
The HDP "strongly" condemned the Arbil attack, calling it an "absolutely unacceptable provocation attempt".
A Turkish soldier was killed and six were wounded in a cross-border operation in northern Iraq against the outlawed Kurdistan Workers' Party (PKK), Turkey's defence ministry said on Friday.
On Wednesday afternoon, the Turkish consulate employee and a civilian were killed while another person was wounded when gunmen opened fire at a restaurant in Kolan Street near the consulate in Erbil, some 375 km north of Iraqi capital Baghdad, according to a statement by the Kurdish Asayish.
In its more than 30-year terror campaign against Turkey, the PKK - listed as a terrorist organization by Turkey, the USA and the European Union - has been responsible for the deaths of almost 40,000 people, including women, children and infants.