The 8,000 capacity stadium at Huntington was due to open in August 2016 but will not be ready for occupation until around December, the club said.
York Council said it would work with the Minstermen to "minimise any impact to the club and its fans".
City said the delay would have "very little impact".
In a statement, it added: "Although some may be slightly frustrated that the club will not be in a position to move into the new stadium for the start of the 2016/17 season, ensuring the future development is built correctly is crucial in providing a fantastic new home for York City for decades to come."
Work on the Jockey Lane site was expected to start in June but the council said it is still finalising contracts.
A spokesman added: "Once these matters are finalised the development phase can commence and work can begin on the stadium itself."
York FC will continue to play at Bootham Crescent until the new stadium is complete.
"The club wish to point out that precedents have been set by fellow football clubs switching stadiums during a season and although some fans may not view it as ideal, the eventual move to the York Community Stadium will be fundamental in securing York City's long term future," the club said.

Wreaths were also laid above the wreck of HMS Royal Oak to mark the 75th anniversary of its sinking.
The warship was torpedoed by a German U-boat while it was at anchor in Scapa Flow in Orkney.
Most of the 1,234 crew were asleep below deck, and 834 - including many boy sailors - died.
The wreaths formed part of the first significant Royal Oak anniversary not to be attended by any of the remaining survivors.
There are believed to be just three men who survived the sinking still alive today.
However, families of the the crew, and the community in Orkney, have vowed to carry on the act of remembrance for generations to come.
The Royal Oak, which also served in World War One, including the Battle of Jutland, is an official maritime war grave.
The memorial service was conducted by the Reverend David Dawson and the Last Post was played by bugler Chris Bray of Her Majesty's Royal Marines Band Scotland.
Relatives of the survivors and those who lost their lives were taken to the site of the wreck by HMS Bangor.
Rear Admiral John Clink said: "It is entirely my honour to have been able to pay tribute to the 834 men who lost their lives in Scapa Flow 75 years ago.
"And we remember, too, those who survived that tragedy, living with difficult memories of their lost friends from that terrible night throughout their lives.
"The Royal Navy will never forget."
Orkney councillor, Dr Stephen Clackson, whose grandfather Seaman Ronald Clackson lost his life at the age of 20, was at the service, which was attended by a number of Royal Navy dignitaries.
"It's important to keep the memory alive," Dr Clackson said. "My son is only three years younger than my grandfather was when he was killed."
"Being aboard HMS Bangor was fascinating and it gave us a picture of what it would have been like for my grandfather, seeing how enclosed it was and the thought of being trapped down there when the torpedo hit."
The White Ensign was exchanged from the wreck for a new one by the Royal Navy's Northern Diving Group from HM Naval Base Clyde last week.
It was later presented to Henry Blythe, whose uncle died on the Royal Oak.
A new £37m home for York City FC will not be finished until part way through the 2016/17 football season.
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More than 100 people attended a ceremony to remember the crew of a battleship which sank in 1939.