There is no extra money to help schools reopen after the summer break, Peter Weir has said.
The news came in a letter to school principals from the education minister.
Some schools had said extra funds were needed for more accommodation or staff to allow all pupils to return to school.
“There is presently no additional funding in the education budget to address the level of pressures anticipated,” Mr Weir said.
The minister said the executive would have to decide if it could make more money available for schools.
Schools have been closed to many pupils since mid-March due to the coronavirus pandemic.
The Department of Education (DE) recently published guidance to enable schools to re-open on 24 August.
Mr Weir said his aim was for every pupil to return to school full-time if it was safe.
However, the guidance said some schools would need to admit pupils on a part-time basis in the first instance.
To enable as many pupils to return for as much time as possible, it said schools could use spaces such as assembly and sports halls and libraries to hold additional classes.
The guidance also said schools could use local facilities such as churches, sports or community halls to hold classes if it was safe.
In the letter, Mr Weir wrote that he did not underestimate the challenges faced by schools in preparing to reopen.
He said the guidance issued by DE was focused on “day one” and would be flexible if the public health position changed.
‘Assessing additional costs’
“Schools, in a number of instances, are reporting that in order to meet my objective, additional funding will be necessary to cover issues such as equipment purchase, sourcing alternative accommodation or bringing in additional staff,” Mr Weir said.
“My department acknowledges that additional support may be necessary (e.g PPE, some additional staffing, etc.) to support the re-opening of schools,” the minister added.
Mr Weir said the Education Authority was attempting to assess the potential additional costs of schools re-opening.
“Options will be brought to me for a view and my department will engage with the Department of Finance to highlight these pressures at the earliest opportunity,” he said.
“There is presently no additional funding in the education budget to address the level of pressures anticipated.
“It is likely that any such bids will have to be discussed at executive level, where they will be considered in the context of the overall funding available and in conjunction with other bids received from across all departments,” Mr Weir said.
Mr Weir concluded his letter by telling principals they would be told of any change in re-opening guidance or funding “as a priority”.