The BBC understands that the Ulster Unionist Party and their executive minister Robin Swann have voted against the budget.
Other parties agreed a spending plan for this financial year with about £14.5bn for day-to-day spending and around £1.8bn for capital spending.
The Department of Health gets the largest share of day-to-day funding - £7.76bn.
The next largest allocations go to the Department of Education (£2.87bn).
The Department of Justice was allocated £1.26bn.
Before the budget Health Minister Robin Swann had warned he needed an extra £1bn to maintain health and social care provision at current levels.
He said there would be "unavoidable real-life consequences for patients, staff and services if health is left with an entirely inadequate budget".
In last year's budget, which was imposed by the Secretary of State Chris Heaton-Harris, health received baseline spending of just over £7.3bn.
First Minister Michelle O'Neill said health had been "prioritised" while Deputy First Minister Emma Little Pengelly said agreeing a budget was "the responsible thing to do".
Ms O'Neill said it was "disappointing" that Mr Swann had not supported the budget.
She said it was regrettable as the executive had a collective job to do.
Deputy First Minister Emma Little-Pengelly said she understood Mr Swann's concerns but added: "The reality is that if the health minister had received what he asked for, it would have consumed the entirety of what additional was available for the budget."
"There are other issues of key importance, special educational needs including broader education, justice. There are competing priorities."
Finance Minister Caomihe Archibald it was also "regrettable" that no department got all the funding they bid for.
She renewed her call to the UK government to review the overall public spending settlement for Northern Ireland.
'Hard choices'
Ms Archibald fleshed out a bit more detail to the departmental allocations.
She said that the Department of Health has been allocated over half of the total budget - including £34m to tackle waiting lists.
The Department of Education will receive about one fifth of the budget, including £25m towards a childcare strategy.
Flagship capital projects like the A6 and Casement Park will receive £180m, and there is £20m for Strule Shared Education Campus.
Ahead of Thursday's meeting Ms Archibald had warned that the budget would be "really challenging" for all departments.
The executive had to approve any budget before it could be put before the Northern Ireland Assembly.
Ms Archibald previously said she hoped the budget would be agreed so that she could engage with the Treasury for further funding.
"We need to be funded properly going forward to allow us to deliver the type of public services people need or deserve," she said.
All departments are likely to face some difficulties when it comes to what to prioritise within their individual budgets.
On Wednesday the new interim chief executive of the Education Authority (EA) Richard Pengelly said the budget was likely to be "incredibly difficult".
He told MLAs that pressures on it would mean "some really hard-nosed choices".
"The brutal reality is we're not going to get the funding settlement that we want or indeed we need." he added.
"But that what we are prepared to do is have conversations about prioritisation."I genuinely worry that in terms of many services we're rapidly approaching the point at which they become unsustainable."
Stormont's finance minister has minimal powers over borrowing and taxation.
So Stormont budgets are primarily about allocating the money which has been sent from London, known as the block grant.
The minister, Caomihe Archibald, has to allocate about £14.5bn for day-to-day spending and around £1.8bn in infrastructure money.
But in the run up to this budget it has been clear that it will not be enough to cover every departmental priority.
The minister had received bids from other departments which were £2bn in excess of the total funds available.
On Wednesday, First Minister Michelle O'Neill said now was the time to strike the budget, to allow money to flow to departments for the financial year.
But she said she and the deputy first minister would continue to press for additional funding from Treasury.
Promising 'the moon and the sun'
Leader of the opposition at Stormont Matthew O'Toole said ministers must be honest and clear with the public about how they are going to prioritise spending within a tight budget.
The SDLP assembly member said Northern Ireland's "terrible" public services cannot be fixed overnight and the public were "mature" enough to understand that choices have to be made.
He said that since Stormont was restored in February all the executive parties had "put down motion after motion where they promise the moon and the sun" without any clarity about how the measures would be funded.
He said his party would prioritise health waiting lists; childcare provision and poverty relief measures.