The National League side has conformed its £8m new Community Stadium will not now be ready to open for next season.
Buckingham Group Contracting is building the new stadium.
The club said it will continue to play fixtures in its current Bootham Crescent home until the new stadium is ready,
A City of York Council spokesperson said: “We understand there will be a delay to the completion of the York Stadium Leisure Complex.
“This would mean a handful of games would not be able to take place in the new stadium as planned and the accompanying leisure facilities will be unable to open as soon as we’d hoped. This is subject to commercial discussions so we cannot comment further.
“A significant amount of progress has been made to date, both on and off site, with all stands now visible.
“We share the disappointment and frustration the delay will cause.
“Work will continue with all partners to minimise any delay and open the York Stadium Leisure Complex as soon as possible, without compromising on quality or safety.”