The civil rights group Liberty is urging parents in England to boycott Thursday's school census amid fears the data will be used to aid deportations.
Parents should refuse to disclose information of children's nationalities and birth countries, said Liberty director Martha Spurrier.
This information was included in the termly census for the first time in September.
The Department for Education called Liberty's claim "absolute nonsense".
Liberty and the campaign group Against Borders for Children wrote to all England's schools earlier this week, urging them to inform parents and guardians that they are under no legal obligation to provide these details.
In addition, the letter suggests that parents also have a right to retract information already given in the autumn survey.
'Education at risk'
Liberty says it fears that the data-gathering exercise will lead families "with uncertain migration statuses to pull their children out of school or fail to enrol them, robbing them of an education and putting their safety at risk".
The Department for Education is adamant that the data collected by schools would not be passed to immigration officials but would instead be used to assess the impact of migration on schools.
However, last month, leaked cabinet letters suggested that Theresa May, as Home Secretary in 2015, had wanted the children of illegal immigrants to go to the bottom of the list for school places, with schools carrying out immigration checks.
And information released later in December to the journal Schools Week under freedom of information law, also suggested that education officials had agreed to share the personal details of up to 1,500 schoolchildren a month with the Home Office.
Liberty says it fears that it is likely that the census information will be used to increase the "matching" of data between the two departments, leading to information such as family addresses being handed over.
Ms Spurrier called the policy "underhanded" and "a nasty new low".
"Every child on UK shores has a right to education - and that right isn't dependent on the accident of their own or their parents' place of birth," she said.
"Clearly we can't expect our ministers to stick up for children's rights.
"But to parents and guardians who believe classrooms should be places of learning, growth and hope for the future, our message today is clear: refuse, retract, resist.
"If enough people refuse to be complicit in building these foreign children lists, the government won't be able to justify harvesting this data."
The DfE said it had repeatedly made clear that the data would not be shared with the Home Office "and there is an agreement in place to this effect".
"The only reason we want parents to return this information is so that we have a clear picture of how the school system is working," said a spokesman.
"For example, being able to assess and monitor the impact that immigration may be having on the schools sector helps us ensure that we are allocating funds where they are needed, and that no groups of children miss out on the education they deserve.
"We take privacy extremely seriously and access to sensitive data is strictly controlled.
"However, the census guidance is clear that parents can withhold information on nationality and country of birth if they choose, and we wrote to all head teachers earlier this month to reiterate this."