They have signed a Parliamentary amendment to the EU Withdrawal Bill dealing with the Government's intention to leave the European Atomic Energy Community (Eurotom).
The transport of nuclear materials, disposing of waste, and carrying out of research is governed by a series of nuclear safeguards that have operated in the UK for four decades through Euratom.
In the Article 50 letter, the UK signalled its desire to leave Euratom at the same time as leaving the European Union.
This has led to a race against time to set up a domestic safeguards arrangement accredited by the International Atomic Energy Agency, a replacement arrangement with Europe, and a series of bilateral deals to replace Euratom's arrangements with key nuclear partners such as the US, Japan, Canada and Australia.
Rachel Reeves is the chair of the Commons Business, Energy and Industrial Strategy select committee, which has issued a report warning the impact of leaving Euratom will be "profound".
It also said it was "highly doubtful" the UK could deliver safeguards to Euratom standards by the date of the UK's departure from the EU in March 2019.
Ms Reeves said: "As a leading member of Euratom, the UK has driven standards and ensured our national interests are front and centre of the development of the industry in Europe.
"But we now face the prospect of setting up our own nuclear safeguarding regime in its place which falls short of Euratom standards.
"This requires us to set up our own bureaucracy, which comes at a cost of millions, with very real doubts that it will actually be ready in time.
"The Government should, as a matter of urgency, be seeking to retain as close as possible an association with Euratom and secure its ongoing delivery of existing safeguards requirements in the UK."
It also said a "no-deal" Brexit would be a "highly risky" option for the civil nuclear sector - which provides 21% of power - in the absence of transitional arrangements.
The MPs called for an extended transitional period for civil nuclear, or the continuation of Euratom support, to ensure standards are maintained and the risks to trade and transport of materials are reduced.
Tom Greatrex, chief executive of the Nuclear Industry Association, said: "The nuclear industry has been clear that leaving Euratom has the potential to cause significant disruption to the industry both in the UK and the EU.
"We welcome the recognition this report, and the evidence the committee received, gives to the validity of these concerns, and the clear message that action must be taken and alternative arrangements put in place before the UK leaves the treaty, to ensure we avoid a damaging cliff edge."