Mr Gulen, who is in self-imposed exile in the US, is accused of establishing and running an "armed terrorist group".
He was once an ally of Turkish President Recep Tayyip Erdogan but has now been accused of plotting to overthrow the Turkish government - a claim the cleric strongly denies.
The US is thought to be unlikely to act on any extradition request.
The move comes amid a national crackdown on perceived supporters of the cleric.
Over 20 journalists working for media outlets thought to be sympathetic to the Gulen movement were arrested last weekend.
Eight of them were freed on Friday on the orders of a court in Istanbul. Those released include Ekrem Dumanli, editor-in-chief of Zaman newspaper.
Four others, including a TV station boss, remain in custody.
According to the BBC's Mark Lowen in Istanbul, it was expected that the authorities would go after Mr Gulen after having targeted those linked to him.
While the US and Turkey have an extradition agreement, the warrant is considered to be largely symbolic - and unlikely to be acted upon.
The relationship between Washington and Ankara has grown fractious, though they remain allies.
Mr Erdogan has faced criticism from international leaders and his opponents, who accuse him of authoritarianism and undermining free press.
Many abroad believe that the charges against Mr Gulen are politically motivated.
The wealthy cleric, who operates an international network of schools and businesses, has lived in self-imposed exile in Pennsylvania since 1999.
According to media reports, the prosecutor filing the arrest warrant accused Mr Gulen of leading an armed terrorist group - a charge that carries up to 15 years in prison.
A Turkish court has issued an arrest warrant for the influential cleric Fethullah Gulen.