The Jewish community is struggling to get kosher meat in time for the Passover festival due to the Northern Ireland Protocol, the DUP has said.
The post-Brexit trade arrangements have also disrupted supplies of specialist cricket soil known as loam from Great Britain.
Extra paperwork has caused a series of bureaucratic obstacles since the end of the post-Brexit transition period.
Northern Ireland has a small Jewish community centred around north Belfast and a central part of the Passover meal is lamb.
First Minister Arlene Foster said: “This is something which is very concerning.
“We have a very small Jewish community here in Northern Ireland. The fact that they cannot access kosher meat is something that would cause me a great deal of concern.”
The Jewish Passover festival begins towards the end of this month and it is one of the most important dates in the faith’s calendar.
The UK Government has unilaterally extended some grace periods associated with the Protocol in a bid to avoid a cliff-edge plunge into extra paperwork.
The Protocol is a post-Brexit arrangement designed to keep the Irish border open by ensuring Northern Ireland continues to follow the EU’s trading rules.
The DUP has vowed to overthrow it over fears it damages the integrity of the UK internal market and Northern Ireland’s place in it.
Mrs Foster told the Stormont Assembly the Protocol was affecting trade and identity for those who view themselves as unionists.
“There is a need not just to tinker at the edges, there is a need to have a replacement of the Protocol.
“There is a need to deal with that urgently because there is damage happening to the economy in Northern Ireland.”
The EU has threatened legal action and described the decision to extend the grace periods as a potential breach of international law.
Mrs Foster said the variation had to happen otherwise some product lines would have quickly dried up.
“I listened very clearly to what the business community want and they do not want the continuation of what we have seen in this Protocol.”
Meanwhile, Ulster Unionist Assembly member and keen weekend cricketer John Stewart has said confirmation that bringing in specialist cricket pitch soil – “loam” – from England is banned because of the protocol is farcical.
He added: “Here we have another example of the EU using a sledgehammer to crack a non-existent nut.
“There is no threat to the European single market or EU plant health standards by continuing the age-old tradition of bringing in ‘loam’ to create, build and maintain cricket pitches throughout Northern Ireland, and the Republic for that matter.
“Groundsmen across the country have been told that it is currently prohibited and it is not an exaggeration to say that this prohibition could threaten the future of cricket here.”