"It's actually not unprecedented for the Turkish authorities to recommend that Turkish nationals not attend the service, it's happened in previous years," he told ABC News Breakfast on Wednesday.
"I'm sure there'll be a very solemn, very respectful commemorative event on the peninsula tomorrow which will be well attended by visitors from mainly Australia and New Zealand."
Turkish nationals, including bus drivers and tour guides, have been barred from the peninsula for the service, The Australian reported on Wednesday.
"Nothing is left to chance and keeping every Turkish person out eliminates a lot of risk," an unidentified official told The Australian.
Mr Chester said Australia had a great relationship with Turkey, despite a diplomatic boilover sparked by President Recep Tayyip Erdogan's incendiary comments last month.
The Turkish leader threatened to send Australians visiting the peninsula home in coffins like their forefathers if any expressed anti-Muslim sentiment in the wake of terrorist attacks at mosques in New Zealand.
Source: Pool Presidential Press Service
The veterans' minister said he didn't want to revisit the spat, other than to note the Christchurch massacres had nothing to do with the 1915 Gallipoli campaign.
"We have enjoyed a great working relationship with local Turkish authorities now for many years," Mr Chester said.
"We greatly respect the way they let us visit their country, put on a commemorative activity which is very moving and a lot of Australians are regarded somewhat of a pilgrimage to go to Anzac Cove on Anzac Day."
Prime Minister Scott Morrison last month welcomed Mr Erdogan toning down his views about Australians after a series of high-level crisis meetings.