The arrested man was from Syria and he was taken into custody in Tekirdag, a province close to the Gallipoli peninsula, a police spokesman told the ABC.
Local media named the man as Abdulkerim H and released a blurred passport photo of him.
Security sources told the ABC the attack was planned in retaliation for Christchurch.
The arrest was the result of a police raid on an alleged Islamic State cell near the Syrian border. A mobile phone was also seized.
A source told Australia's news.com.au that police believed he was planning to bomb the service or drive a car into the crowd.
Police evacuated the Gallipoli site and were conducting a thorough search to check for bombs in the area just hours before the dawn service was due to begin.
It follows inflammatory comments made by Turkish President Recep Tayyip Erdogan after the Christchurch terror attack last month. Erdogan said New Zealanders and Australians who travelled to Turkey with bad intentions would be returned in coffins like their ancestors at Gallipoli.
He also repeatedly used, at a campaign rally, footage of the mosque massacre that killed 50 people.
Fifty other people were injured in the attacks, which occurred during Friday prayers.
Every year, Australians and New Zealanders travel to Turkey for memorial services commemorating the 1915 Anzac military campaign to drive Ottoman troops from Gallipoli and the Dardanelles region.
Soldiers from New Zealand, Australia, Turkey and other countries held several services at Gallipoli on Wednesday, ahead of Thursday's dawn service marking the landings.
The police spokesman did not specify which day the detained suspect may have been planning to carry out the alleged attack.
Turkey has said Islamic State was responsible for several bombings that took place in 2015 and 2016, which killed some 200 people in total. Although the militant group has not been active in Turkey of late, authorities still carry out routine operations against suspected Islamic State members.
