Nicola Richards said the Brexit select committee, which she sits on, was no longer needed as Brexit was "ultimately a thing of the past".
The cross-party committee has been chaired by Labour MP and avid Remainer Hilary Benn since it was formed in 2016, with the aim of scrutinising Britain's departure from the EU.
Leader of the House, Jacob Rees-Mogg, has called for the group to be disbanded after its current cut-off date of January 16.
He said in a letter: “There will be plenty of opportunities for questions, statements and debates, as well as the detailed analysis of the House select committees in the months ahead.
"Whilst this is ultimately a matter for the House, it is the view of the Government that your Committee’s work should come to an end in line with the current temporary standing orders, which were agreed by the House.”
West Bromwich East MP Ms Richards, who was appointed to the committee last year, said: “This is completely the right decision as Brexit is ultimately a thing of the past.
“Any issue can be looked at and scrutinised through the prism of existing select committees, which is the way we look at our relationship with any other continent or country.
“It has been a privilege to serve on the committee, but we have now exited the transition period with a good deal and it’s time to move on.”
Mr Benn has called for the committee to continue until June to scrutinise the EU trade agreement and the early stages of the new relationship.
Last year it was renamed the committee for the Future Relationship with the European Union after Britain had left the bloc.
A number of West Midlands MPs have served on the committee, including current members Jane Stevenson (Wolverhampton North East) and Gary Sambrook (Birmingham Northfield).