Trade talks after leaving the EU will need more UK officials with language skills, say the All Party Parliamentary Group (APPG) on Modern Languages.
There is already a languages skills shortage but currently the UK can rely on other EU nationals "to plug the gap", say the group.
Ministers say their reforms are already boosting language learning in schools.
Launching a checklist on Brexit and languages, the group say lack of language ability loses the UK an estimated 3.5% of economic performance.
The country currently relies on the EU to negotiate trade deals but this will no longer be possible once the UK has left the Union, they add.
APPG co-chair Baroness Coussins said: "Brexit must make the UK's language skills a top policy issue.
"Language skills are vital for our exports, education, public services and diplomacy."
Baroness Coussins called for "a national plan to ensure the UK produces the linguists we need to become a world leader in global free trade and on the international stage."
The group identify a need to boost skills in both European and non-European languages for the purposes of trade, international relations and security.
In particular, they fear the loss of European language skills if EU nationals already living in the UK are not guaranteed residency status post Brexit.
They also want the UK to continue full participation in the Erasmus+ scheme, where young people study, work volunteer and train abroad in Europe, some working as language assistants in schools.
The checklist includes calls to:
"It is essential that schools continue to be able to recruit EU nationals post-Brexit," said Malcolm Trobe, interim general secretary of the Association of School and College Leaders.
"There is already a critical shortage of language teachers and the last thing that we need is anything which makes this situation worse.
"We understand that Brexit means Brexit but it is vital that it does not also mean a full-blown crisis in language teaching."
Mike Buchanan, head of Ashford School and chairman of the Headmasters and Headmistresses Conference, said independent schools were proud of their "increasingly central role in ensuring the survival of languages in British universities".
"But more is needed to reverse this trend. The national situation is parlous," said Mr Buchanan.
Sara Davidson, head of modern languages at the private Oundle School and chairwoman of the Independent Schools Modern Languages Association, said she did not know of a language department that did not employ native speakers.
"Native speakers are helping us out amidst a major recruitment crisis in modern language teaching.
"We simply do not currently produce enough linguists in this country to fill the modern language teaching vacancies we have."
Ruth Sinclair-Jones, UK director of Erasmus+, said the value of the scheme to the UK "cannot be underestimated".
"Losing UK participation would limit the future prospects of young people and the country as a whole," she said.
And Mark Herbert, head of schools programmes at the British Council, said: "Learning a language isn't just a rewarding way to connect with another culture but boosts individual job prospects, as well as business and trade opportunities for the UK."
A Department for Education spokeswoman said government policies meant the number of students taking one language at GCSE was up from 40% in 2010 to 49% this year.
The spokeswoman added: "The UK's future access to the Erasmus+ programme will be part of wider discussions with the EU.
"Existing higher education UK students studying in the EU will continue to be subject to current arrangements."
The government must plan now to avoid a post-Brexit languages crisis, say a cross-party group of MPs and peers.