Some are having to hire cars and taxis to fulfil sports fixtures or take field trips as a result.
Principals have been warned by the Education Authority (EA) that some teachers who currently drive minibuses may be doing so illegally.
The EA said the change was due to the Driver and Vehicle Agency clarifying the rules on minibuses.
However, one principal told the BBC the change would have "huge implications" for schools.
Previously, staff who held a licence which qualified them to drive a car would also have been able to drive a school minibus.
However, revised guidance from the Driver and Vehicle Agency (DVA) states that teachers must now have a D1 licence and a driver's qualification card to do so.
The EA letter to principals, issued in June, states that if this is not the case there will be serious consequences.
"If this criteria cannot be met, any journey undertaken by staff will not be considered legal and may leave the driver and the employer facing prosecution and penalties," it states.
"It is imperative that the school at all times and you satisfy yourself that the relevant criteria have been met before authorising employees to drive a minibus."
The principal of Lisneal College in Londonderry, Michael Allen, said the new restrictions were having a serious impact.
"No-one at my school currently meets the new criteria," he said.
"I am now having to pay for taxis to take pupils on geography field trips before the end of term.
"A school team was also due to play a cricket match which we were about to cancel until another school, who had a qualified driver, helped us out.
"This change could end up costing my school up to Â£1,000 before the end of term alone."
In a statement, the EA said it had written to all schools to make them aware that DVA had clarified the licence requirements in relation to minibuses".
"These requirements apply to those employed in schools who drive minibuses."
The DVA has not yet responded to a request for further details.

The house, which is now a museum in Haworth, West Yorkshire, reopens after a refurbishment on Friday.
"It's closer than it's ever looked to how it would have done in the Bronte period," said Bronte Parsonage Museum collections manager Ann Dinsdale.
"Charlotte put her stamp on the house, and there's quite a lot of colour."
Researchers from the University of Lincoln examined sections of the walls, and in some places found 18 layers of paint and wallpaper dating back to the sisters' habitation in the mid-19th Century.
Source: BBC History
"They came up with the strata, all the layers of paints that had been used over the years in the parsonage and they were able to work out which was the Bronte period," Mrs Dinsdale said.
"All the historic rooms, which are part of the original parsonage, have been completely redecorated."
Charlotte, Emily and Anne Bronte lived with their father and brother in the parsonage. Enduring literary masterpieces written there include Charlotte's Jane Eyre and Emily's Wuthering Heights.
The sisters are particularly remembered for their depictions of the surrounding bleak landscape and their characters' emotional turmoil.
"I think people are possibly going to be quite surprised when they visit the parsonage," Mrs Dinsdale added.
"People have this image of [it] being quite austere with white and grey walls. Actually, it's very clear that they did experiment with colour."
Schools are facing new restrictions on which teachers can drive school minibuses.
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The former home of the Bronte sisters has been returned to the design of the authors' era after researchers found fragments of its original decor.