"Claims regarding interference in the processes of referee classification, assignments, scoring and appointments, as well as in the examinations on rules, have been investigated," he wrote on X.
Among those arrested was Ferhat Gundogdu, president of the refereeing body, and his vice-president, with searches carried out at all of the suspects' "homes, workplaces and offices".
"We will steadfastly continue the fight for clean football so that claims undermining trust in Turkish football are clarified (and) those responsible are held accountable," Gurlek said.
The move comes a year after Turkey's Football Federation (TFF) suspended 149 referees over allegations of involvement in an illegal betting scandal.
In a statement on its website which did not mention the arrests, the TFF said it was "working resolutely" to restore public faith in "clean football".
Without making a direct link to the earlier scandal, the TFF said it had "resolutely tackled the issue of betting and illegal betting", fully supporting the work of the interior, justice, and youth and sport ministries, and that "the investigation and cooperation process with (them) is still ongoing".
All documents requested by investigators "have been sent.. in sealed envelopes, with a request for delivery to the Forensic Medicine Institute for fingerprint and DNA analysis and other necessary examinations," it said.
Newspaper Hurriyet said prosecutors believe the suspects improperly influenced referee classifications, promotional exams and match appointments through document fraud and systemic intimidation.
It said the probe was opened following a formal complaint, with investigators looking into financial audits and phone records alongside witness testimony and expert reports.
During last year's referee scandal, a TFF investigation found 371 of Turkey's 571 referees officiating in the professional leagues had betting accounts and 152 of them actively placed bets.
Police arrested 29 people in the sprawling scandal, among them 14 footballers -- one of whom was Fenerbahce's international midfielder Mert Hakan Yandas.
Authorities suspended more than 1,000 players, including 25 from the first division.