Labour’s David Lammy, who has been at the forefront of efforts to help those caught up in the row, posted a screenshot of the typed message on his Twitter account.
“Be Grateful Man for the Country that gave you a Life, and stop Knocking it,” a section of the letter, dated 16 April, reads.
“Otherwise, Go back to your Country of your Forbears [sic] and lets [sic] be rid of you.
“If you cannot say good about us, then go back, it is as simple as that.”
In his response, north London-born Mr Lammy urged the writer to “learn your history” and said he would continue to campaign for Windrush families.
The MP for Tottenham said: “I have just received a letter telling me to be ‘grateful’ as a black man for all ‘we have done for those black people who came to live here’, or ‘go back to where ever you came from’. I was born in the Whittington Hospital the son of Windrush migrants. And I will speak for them.
“And let me be clear, following the 1948 Nationality Act my parents and the Windrush generation were invited here as British citizens. Learn your history. Citizens have been retrospectively renamed as “immigrants” as a result of legislation and policy pandering to far-right rhetoric.”
Mr Lammy has called for compensation for those affected, telling a packed meeting in Parliament last week that an apology was not enough.
The Windrush generation are named after the cruise ship that brought one of the first large groups of West Indians to Britain, as the country sought to rebuild after the Second World War.
Anyone who entered the UK before 1973 is legally entitled to live in Britain, but many of the Windrush generation have recently suffered issues as a result of tightened UK immigration requirements introduced when Mrs May was home secretary.
Their problems include difficulties when finding work, getting NHS care, accessing benefits, or trying to secure housing, as they do not have the correct documentation to prove they are entitled to live in the UK.
Ministers have insisted they are yet to find evidence to confirm reports that some have been wrongly deported.
The Government has vowed to resolve cases within two weeks, with the Prime Minister saying “we have no intention of asking anyone to leave who has the right to remain here”.
Home Secretary Amber Rudd has said Windrush families who have “suffered loss” because of failures over their immigration status will receive compensation.