0144 GMT December 16, 2019
The warning comes in a letter from the finance director at the Department of Education (DE), Gary Fair, BBC wrote.
Fair also wrote that education faced a ‘challenging’ outcome from the Northern Ireland budget.
However, he said there would be an extra £7.25 million for the Aggregated Schools Budget (ASB) in 2019-20.
That is a 0.6-percent rise on the £1.167-billion funding to schools in 2018-19.
Schools will also receive an additional £54.6 million specifically to pay for an increase in public sector pension costs — including teachers — which is to take effect on April 1.
The ASB is the money that goes directly to more than 1,000 schools funded by the department.
The money a school receives each year is based on a number of factors, including the number of pupils it has, the number of pupils with additional needs and the size of the school buildings.
About 80 percent to 90 percent of a school's funding is normally used to pay staffing costs, including teachers and classroom assistants.
Fair said that the department would be able to maintain the amount of funding schools received per pupil at current levels.
That follows reductions in recent years.
Schools have also had their individual financial allocations for 2019-20 confirmed.
'Do not underestimate challenges'
"It is essential that all school budgets are managed on the assumption that there will be no further in-year allocations from the department during the 2019-20 financial year," Fair wrote.
"I fully appreciate the difficulties that this budget outcome will mean for schools and I do not underestimate the challenges ahead."
The Northern Ireland Audit Office has previously said the aggregated schools budget had decreased by 10.4 percent in real terms since 2012-13.
The Education Authority has also said that almost half of Northern Ireland's schools will be in deficit this year.