Nicoletta Peddis, who is Italian, posted yesterday on Twitter a picture of the letter sent to her home telling her "we have won Brexit" and that "we won't be happy until you leave".
It wrote that "we dont need foregneirs [sic] taking our housing our jobs our GP places".
Ms Peddis, who works for Nestlé, later said she shared the letter on social media "to turn the pain and the anger into words and help me deal with the ugliness of the times we live in".
She said her neighbours, a Romanian couple, had also received the same note and that police were investigating to find if it had been sent to anyone else in the area.
North Yorkshire Police has since confirmed it is looking into the incident as a hate crime.
The force’s Neighbourhood Policing Inspector Andy Godfrey said: “Targeting hate at a person because of their race, religion, disability, sexual orientation or gender is a crime which can have a devastating impact upon individuals and whole neighbourhoods, and will not to be tolerated in North Yorkshire.
“We understand that these letters in York have caused concern and we want to assure those affected, and those in the wider community, that we are taking this matter very seriously and are determined to find who is responsible for sending them.”
York City Council has meanwhile said it was "horrified" by the letter and its contents, and urged anyone else who had been sent it to come forwards.
Coun Darryl Smalley, Executive Member for Culture, Leisure & Communities at City of York Council, said: “This is unacceptable in York or anywhere else, and we’re horrified to see this.
"This is not in the spirit of York, which staunchly welcomes and appreciates the contributions to the city of all who have chosen to make York home.
"My heart goes out to those receiving such hateful mail and I am glad to see that they are being reported to North Yorkshire Police. Anyone receiving letters like these, or experiencing any other hate crime, should report it to the police who can also offer support.”
Anyone with information that could assist the investigation, including anyone who has received a similar letter, is urged to please call North Yorkshire Police on 101 or email [email protected] quoting reference number 12210141001.