A sign bearing the title "Happy Brexit Day" was reportedly found stuck to fire doors on Winchester Tower in Norwich on Friday morning.
The discovery came hours before the UK officially left the European Union at 11pm on Friday.
A photo of the poster shared in news reports and on social media revealed it declared: "As we finally have our great country back we feel there is one rule that needs to be made clear to Winchester Tower residents.
"We do not tolerate people speaking other languages than English in the flats.
"We are now our own country again and the Queens English is the spoken tongue here.
It then goes on to explain the government will soon "implement rules that will put British first" and finishes with "so best evolve or leave."
News of the poster circulated on social media. Sharing a photograph of the poster, one Twitter user said: "My friends' friend had this stuck on their flat door in London. They woke up to this vile and racist message. In one of the most diverse cities in the UK. You cannot tell me that Brexiteers are not racist."
Writing on Twitter on Saturday, Norwich City Council said: "You may have seen a photo of a poster that has appeared in one of our properties.
"Norwich has a proud history of being a welcoming city, and we will not tolerate this behaviour.
"As soon as we became aware of this incident, we reported it to @NorfolkPolice and they are investigating.
"We take this very seriously and encourage residents to contact us or the police if they have any concerns."
According to the BBC, which spoke to a resident, the signs were left on fire doors across all 15 floors of the block of flats before being removed by the caretaker.
Mike Stonard, a cabinet member on Norwich City Council, told the Eastern Daily Press: "I absolutely condemn this abhorrent poster. Whoever put it there has committed a hate crime, it is as simple as that.
"Many people voted for Brexit for a range of different reasons, however I am sure not many of them will condone this kind of thing."
Norfolk Police have been contacted for comment.