The pilot project, which will be established on the site of Medway Secure Training Centre (STC) in Kent, had been due to launch in autumn 2020.
But the Ministry of Justice has told CYP Now that due to "a number of complex issues", it is now unlikely that it will be ready to open by then.
Details of the delay were revealed by the organisation contracted to run the secure school - Christian youth charity the Oasis Charitable Trust.
In the November edition of the Association of Youth Offending Team Managers' newsletter, Steve Chalke, founder of Oasis said the establishment will not be open until 2021.
In relation to the delay, he said "the problem with the Medway site is that it is a prison and they want to make it a school and a home that you can relax in".
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An MoJ spokesman said the government had anticipated opening the first secure school towards the end of 2020, but that is now likely to be later and a date will be confirmed "in due course".
"We are working with Oasis, and our other partners - the Department for Education and NHS - to bring forward a revised timetable as soon as possible," the spokesman said.
"A number of complex issues have taken longer to resolve than originally anticipated and we are working with all partners to resolve these."
Plans to pilot two secure schools were first announced in December 2016, on the back of recommendations made in Charlie Taylor's review of the youth justice system.
Their aim is to place a greater focus on the education and rehabilitation of young offenders, improving safety in the youth secure estate and reducing reoffending.
In 2017, then youth justice minister Phillip Lee said they could be up and running by the end of 2019, and potentially rolled out nationally within 10 years.
Earlier this week, a coalition of more than 70 children's organisations called for all prisons for children, including young offender institutions and STCs, shut down.