The note, which had not been approved by senior figures at St Winefride's primary school in Newham, suggested youngsters in one year 2 class arrive in "dirty and worn out" clothes.
Writing on the school's website, head teacher Paul Underwood responded: "I have issued a letter to 2N parents regarding the revised Black History Month presentation.
"Once again, I apologise on behalf of the school for Friday's unauthorised letter and the offence caused."
According to the Newham Recorder, the letter said: "It might be an idea to not wash these clothes and stain them with tea or coffee to look more authentic."
Though pointing out the letter was "rogue", one parent told the local newspaper: "You wouldn't ask Jewish children to come in and re-enact the Holocaust."
A spokeswoman told the Recorder: "We understand the importance of Black History Month and celebrate this by studying the success and achievements of black role models.
"The content of this letter is not in keeping with the ethos of the school or a reflection of how the school celebrates Black History Month."
Celebrating its 30th anniversary in the UK this month, Black History Month recognises the contributions African, Asian and Caribbean people make to the country's politics, economy and wider culture.