Caroline Nokes said EU nationals already living here will be able to apply to stay under the EU Settlement Scheme and have until June 2021 to do so.
But she admitted businesses will struggle to distinguish between those already here and new migrants, adding that employers must check if EU citizens have the right to work in the UK, if Britain leaves the bloc without a deal.
Ms Nokes told Parliament that employers will not need to carry out additional checks – prompting confusion among MPs about how industry leaders will know who can work here until the scheme ends in 2021.
This paves the way for freedom of movement to continue until new immigration rules are enforced.
Hilary Benn, chairman of the Brexit Select Committee, said: “If the UK leaves the EU in March with no deal, and if, as the minister has told the House this afternoon employers will not be required to make any additional checks, other than asking for an EU passport, then the minister has in effect told the House that free movement will continue after we have left the EU.”
Ms Nokes told MPs: “We are seeking a sensible transition period. But the Prime Minister has been very clear, free movement will end and we will in due course set out the future immigration system which will enable there to be further clarity.”
Tory MP Jacob Rees-Mogg stressed Brexit must mean Britain can take control of its borders.
Ms Nokes said: “As part of Brexit we will end free movement which will give us back control of our borders. This is what the people voted for.”
Home Secretary Sajid Javid said: “If there was a no-deal – if – we won’t be able to immediately distinguish between those Europeans that were already here before March 29, and those who came after and therefore I wouldn’t expect employers to do anything different than they do today.”