The Princess, who is married to the Queen’s cousin, was captured by photographers outside Buckingham Palace in London wearing a blackamoor jewelled brooch to the gathering on Wednesday.
The event included almost all members of the house of Windsor, including the Queen, Prince Philip and Prince Charles, as well as Markle, who became engaged to Prince Harry last month and describes her heritage as bi-racial.
TMZ On Friday quoted a spokesperson as saying Princess Michael was”very sorry and distressed” over the incident and had vowed to never wear it again.
It is believed to be the first time the Princess, 72, had met the US actor, who has spoken before of the racism she, and her mother, Doria Ragland, who is black, have faced.
Blackamoor jewellery has been criticised for evoking “racial crusades” and for promoting imagery which is now considered racist, with the term blackamoor itself considered a term of abuse.
The Oxford English Dictionary describes the word blackamoor as an archaic noun dating from the 1500s, which means: “A black African or a very dark-skinned person.”
Critics say blackamoor figures and jewellery can depict those of black African descent in subservient roles such as footmen and serving staff, furthering harmful stereotypes.
They are often shown wearing turbans with sparkling jewels. They can be carved from ebony or porcelain painted black.
A petition against one such figurine in the lobby of a hotel in Australia states: “Frequently, these items reflect racist ideas about black people through offensive and dehumanising caricatures.”
The Princess has been criticised for her choice on social media.
Marnie O’Neill tweeted: “What kind of person makes a decision like this?”
While Sam McArther said: “Princess Michael’s brooch was disturbing and hurtful. They need to contain her and educate her on moral issues. She is not above any culture or race. As a royal we expect better.”
HuffPost UK has contacted Princess Michael for comment.
It is not the first time the Princess has been at the heart of a racism row.
In 2004, she was accused of telling a group of black diners in New York to “go back to the colonies” after a dispute.
The Princess strongly denied the claims.
But defending herself at the time, she said of her travels in Africa: “I even pretended years ago to be an African, a half-caste African, but because of my light eyes I did not get away with it, but I dyed my hair black.
“I travelled on African buses. I wanted to be a writer. I wanted experiences from Cape Town to right up in northern Mozambique. I had this adventure with these absolutely adorable, special people and to call me racist: it’s a knife through the heart because I really love these people.”
After accepting Prince Harry’s proposal in November, Markle, 36, became the first non-white member of Britain’s modern Royal family, a milestone she will complete with their marriage next year.
Asked last month about a focus on her ethnicity, which led the Prince, 33, to issue a strong statement to media last year, Markle said: “Of course it’s disheartening.. at the end of the day I am proud of who I am and where I come from.”