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.
A new £37m home for York City FC will not be finished until part way through the 2016/17 football season.