So far, 18 of the 21 suspects have been detained, state-owned Anadolu news agency reported.
The move comes a week after the Turkish Football Federation (TFF) suspended 149 referees and assistant referees after an investigation found the officials working in the country's professional leagues were betting on football matches.
The Istanbul chief prosecutor's office said the detention of the 17 referees was on the grounds of abuse of duty and manipulating match results. A Super Lig club president, a former club owner and a former association president were also ordered detained over alleged match-fixing, it said.
One more person faced arrest for spreading misleading information on social media as part of the operation across 12 cities in Turkey, the statement said.
In its own separate probe, the TFF's disciplinary board has imposed bans ranging from eight to 12 months on 149 officials for involvement in betting activity.
TFF President Ibrahim Haciosmanoglu has described the situation as a "moral crisis in Turkish football". Its probe revealed that 371 of 571 active referees in Turkey's professional leagues had betting accounts, and 152 of them were actively gambling.
One referee had bet 18,227 times, and 42 referees had bet on more than 1,000 football matches each. Others were found to have bet only once.