The movement denies it is a "terrorist organisation", saying it is a peaceful group promoting education and charity.
Dogan Holding chief legal advisor Erem Turgut Yucel and former chief executive Yahya Uzdiyen were detained after police raided their offices and homes, the company said in a statement to the Istanbul stock exchange.
Dogan Holding is one of Turkey's biggest conglomerates with interests in retail, tourism and media including the Hurriyet daily, Dogan news agency and broadcaster CNN Turk.
"They were detained as part of the investigation in which our Ankara administrative representative Barbaros Muratoglu was arrested," the company said.
Muratoglu was charged last month with "aiding an armed terror group FETO" -- which refers to "Fethullah Terrorist Organisation" -- the name Turkish authorities give to the movement led by Fethullah Gulen.
Dogan Holding insisted searches were made only of the aforementioned executives' personal offices after Turkish media reported the company's Istanbul offices were the subject of police raids.
"Our holding and subsidiaries' activities are not affected," the company said, adding work continued as before "without interruption".
Islamic preacher Gulen -- currently in self-imposed exile in the United States -- denies Turkey's accusations that he ordered the failed July 15 coup.
And the movement denies it is a "terrorist organisation", saying it is a peaceful group promoting education and charity.
Since July, over 41,000 people have been arrested after parliament imposed a state of emergency a few days after the attempted overthrow of President Recep Tayyip Erdogan.
The controversial state of emergency was extended Tuesday for another three months.
More than 100,000 people from the civil service, judiciary, military, media and education sector have been detained, dismissed or suspended over alleged links to the coup-plotters.
Ankara has come under heavy criticism over the widescale purges but the government insists it is dealing with a real threat, saying it must remove Gulen supporters from the state.