Detention orders had been issued for 1,000 people, of which 803 had been detained, the sources said, in operations carried out across all 81 of Turkey's provinces.
German foreign ministry spokesman Sebastian Fischer on Wednesday criticised the mass detention saying: "We don't believe arresting 1,000 people so long after the putsch is really proportionate".
Gulen, self-exiled in the United States for more than a decade, denies his involvement in the failed coup in July 2016 and repeatedly denounced the brutal persecution of his followers, which he calls a true witch hunt.
Dozens of police officers were among those detained for alleged links with US-based cleric Fethullah Gulen.
"We are trying to cleanse members of FETO inside the armed forces, inside the judiciary and inside the police", he said, using an acronym for the label, Gulenist Terrorist Organisation, which the government has given to Gulen's supporters.
The referendum bitterly divided Turkey.
10 killed, 13 injured in bomb blast in Pakistan's tribal belt
The injured included four Khasadar official who were on way to perform census duty. Another attack at the town's vegetable market in January killed at least 20 people.
More than 47,000 people have been arrested since the coup, Mr Soylu has said, including some 10,700 police officers and 7,400 military personnel.
Another 2,200 were being sought as authorities targeted what they said was a secret structure within Turkey's police force.
Prime Minister Binali Yildirim had hinted in a television interview this month that a new anti-Gulen crackdown has been in the pipeline.
Turkey's main opposition party - the secular Republican People's Party, or CHP - said on Wednesday it would challenge the outcome of the referendum at the European Court of Human Rights a day after a high court rejected its appeal.
Turkey crackdown: Has Erdogan gone too far? Ankara said it had informed the U.S. and Russian Federation before the strikes.
The Council of Europe's parliamentary assembly angered Turkey on Tuesday by placing the country under review and calling for urgent measures to restore freedom of expression and the press.