A letter from the school said staff, students and parents are "devastated" that the board has objected to the college moving into the new accommodation on the first day of the new school term.
A statement from Hazelwood said the BELB has padlocked all access gates.
"An administrative and protracted issue over the lease of adjacent, adjoining and derelict land to the college that is owed by BELB is cited as the problem," they explained.
"BELB had indicated previously that they would not be the cause of any delay in this issue.
"Hazelwood College had reasonable expectation of possession of the time-bound lease by the start of this new academic year."
The mobile classrooms were financed privately by Hazelwood and staff had been working over the past few weeks to prepare the mobiles for the new school year.
As the board still owns the property, any use of the unapproved building may place a health and safety risk to pupils, staff and the general public.
However the Belfast Education and Library Board has said they have taken the measure due to health and safety as the current premises has not met appropriate planning procedures.
A spokesperson said they received a written request from Hazelwood College in May requesting consideration from the board to acquire a lease in relation to the site.
"However, it was reinforced that the acquisition of the proposed lease needed to be compliant with the board, Department of Education, Belfast City Council Building Control and Department of Environment approvals," a statement explained.
"In the interim, it was inappropriate to commence any work on the site, as this was still board property. In that regard, it was made clear that this would not be achievable in September 2013."
The board spokesperson said after a recent site visit they noted the building that had been erected without appropriate approvals and have been in regular contact with the Board of Governors regarding regulation compliance.
Principal Kathleen Gormley said the new accommodation is for sixth form students as well as children with special needs.
"No school principal wants to send home 200 of our sixth form on the first full day of the school year. I thought it would be better to bring our students in today and explain the situation face-to-face," she said.
She said that both planning permission and building control approval has been obtained for the accommodation and there was no health and safety issue.
"I was told if we moved ahead with approvals of planning permission and building control that the board would not, and I quote, 'would not stand in our way'.
She said she was dealing with "two levels of bureaucracy and sometimes one doesn't seem to understand the other".
SDLP North Belfast MLA Alban Maginness described the situation was "bizarre".
"Students are being prevented from using a new facility for Hazelwood," he said.
"This is a ludicrous situation where the school has gone to a lot of expense to provide additional accommodation for its students who are actually being prevented from being educated."
He said he would lobby on behalf of the school to find a resolution.
North Belfast DUP MLA Nelson McCausland said he was deeply concerned that the new school year has been disrupted.
"Clearly this dispute, which has already resulted in the school having to close early, is having a detrimental impact on the education of pupils," he said.
"This is very disappointing and I call for a concerted effort by all relevant parties to find a working solution in the short term and to expedite and resolve outstanding issues."
Meanwhile the school staff say they hope an interim solution can be put in place for students.