It must not become a school's job to identify and help EU families and staff apply for permission to live and work in the UK after Brexit, a union has warned.
The NAHT headteachers' union said it was concerned about "unintended consequences" if schools became involved in the process.
The union argued that it should be the role of school leaders to simply signpost those who may need to apply for permanent leave to remain in the UK through the EU Settlement Scheme.
The Department for Education (DfE) says schools should help staff, parents and carers by directing them to the support and resources that have been made available.
Ian Hartwright, NAHT senior policy adviser, said it must be clear that it is not for schools to try to identify individuals who need to apply for settled status, adding: "Really, their role is to signpost anybody who needs help to government-produced materials."
He added: "We think there is a real risk of unintended consequences if schools are asked to [do] anything else other than that, because it could result in children going missing from education.
"Not all EU migrants are highly skilled individuals who will find these things easy to navigate. We wouldn't want any repeat of Windrush or hostile environment stuff where people might be fearful of engaging with authorities around that."
Mr Hartwright said the union had been given reassurances by government that there is plenty of help available to people who want or need it, and that there will not be a "hostile environment situation around this".
Schools' preparations for Brexit
The DfE has published guidance online for schools in England on preparing for Brexit.
The advice says schools should let staff who are citizens of the EU, Iceland, Liechtenstein, Norway or Switzerland know that they need to apply to the EU Settlement Scheme in order to continue living in the UK after 2020.
It also says that schools should continue to offer places to children who are citizens of the EU, Iceland, Liechtenstein, Norway or Switzerland.
The Association of School and College Leaders (ASCL) has also raised concerns about the impact of Brexit on schools, particularly on foreign language departments.
The union's general secretary, Geoff Barton, said: "Two-thirds of state schools and 79 per cent of independent schools have one or more staff from EU countries, according to a recent survey by the British Council. This supply line is vital.
"Language teaching is in crisis, with severe teacher shortages and a long-term decline in French and German entries at GCSE and A level."
He said that it is "essential that the post-Brexit visa system is as supportive as possible to recruiting staff from EU countries and does not create hurdles which worsen the pressure on language teaching".
Mr Barton added: "The other area of concern is around the implication for pupils from EU countries.
"While many families will have applied for the EU Settlement Scheme and intend to remain in the UK after Brexit, it seems likely that some families will leave the country.
"We don't know how many will do so, but this may have a social and educational impact on pupils moving away from their school and friends, as well as implications on school funding because it is allocated on a per-pupil basis."
The DfE has said that there will be no change to immigration or right to work arrangements for teachers from the EU, Iceland, Liechtenstein, Norway or Switzerland arriving in the UK until 31 December 2020, or any change to the recognition of their qualifications.
Arrangements for recognition of professional qualifications after 31 December this year are subject to further negotiations between the UK and EU, the department said.