First Minister says issues about symbolism and practicality
The Military of Defence has insisted the Northern Ireland Protocol places no limitations on its operations.
It comes as the UUP MLA Doug Beattie - a member of the Army reserve - said 15 days' notice was required and additional paperwork, in order for it to move personnel and equipment across the Irish Sea from GB.
He explained that while an individual may not be restricted, a soldier could not be properly deployed, if they did not have their equipment.
"If the military had to surge forces into NI - and this is just an example - for whatever reason under these rules and regulations they would not be able to do so," he told the BBC.
"It is more than just symbolism."
He added: "Worryingly, there will also be a need to complete a NATO form before any movement takes place.
He said the NATO form was usually required to move troops and equipment around the world.
First Minister Arlene Foster said it was one of a number of issues the protocol had brought up. She said she would be working with the Defence Secretary Ben Wallace on Friday on the matter.
She said the matter was both about symbolism and practicality.
"The UK military has to work at speed within its own jurisdiction," she said.
"The EU should not be able to intervene with the sovereign nature of the military within the United Kingdom."
Doug Beattie has written to the Secretary of State Brandon Lewis calling for urgent action. He said if barriers could not be removed, he should move to invoke article 16 of the protocol - a safeguard should difficulties arise in its operations allowing either the EU or the UK to take appropriate measures.
Since the EU and UK formally severed ties at the beginning of the month, Northern Ireland has continued to follow some of the EU’s rules to prevent the establishment of a hard border on the island of Ireland.
Hauliers have faced difficulties transporting stock to Northern Ireland from the rest of the UK. While retailers have struggled to fill shelves.
The UK Government has said the disruption is down to the border hold-ups over Christmas between France and the UK when a new coronavirus variant was found in England.
"It is ludicrous where UK armed forces cannot move around the UK with equipment without permission," added Mr Beattie.
"This is quite incredible and I simply cannot believe that any UK government would tolerate such a situation."
He added: "Every MP should be up in arms."
In a statement, the MoD said: "The Northern Ireland Protocol has not placed any limitations on the Ministry of Defence's ability to conduct operations."