The Palace said it took the incident, at the Queen Consort’s reception on violence against women on Tuesday, “extremely seriously” and had investigated immediately.
Ngozi Fulani, chief executive of Sistah Space, detailed the conversation on Twitter, describing it as a “violation” and said the experience will “never leave me”.
Ms Fulani said the household member challenged her when she said her charity was based in Hackney, east London, saying: “No, what part of Africa are YOU from?”
The Palace said in a statement: “In this instance, unacceptable and deeply regrettable comments have been made. We have reached out to Ngozi Fulani on this matter, and are inviting her to discuss all elements of her experience in person if she wishes.
“In the meantime, the individual concerned would like to express her profound apologies for the hurt caused and has stepped aside from her honorary role with immediate effect.
“All members of the Household are being reminded of the diversity and inclusivity policies which they are required to uphold at all times.”
Mandu Reid, leader of the Women’s Equality Party, who was next to Ms Fulani and witnessed the exchange, told the PA news agency they were treated like “trespassers”.
Ms Reid said: “We really felt ‘Oh, OK, we’re being treated almost like trespassers in this place’.
“We’re not being treated as if we belong, we’re not being embraced as if we are British.”
She described the exchange as “grim” and like an “interrogation”, adding: “She was really persistent. She didn’t take Ngozi’s answers at face value.”
Ms Fulani detailed the full conversation, which she said happened 10 minutes after she arrived in the Palace’s Picture Gallery, on Twitter, which included the exchange: “Where are you from?’
“Me: ‘Here, UK’. ‘No, but what nationality are you?’ Me: ‘I am born here and am British.’ ‘No, but where do you really come from, where do your people come from?’ Me: ‘My people’, lady, what is this?’
“Oh, I can see I am going to have a challenge getting you to say where you’re from.”
Ms Fulani, who founded Sistah Space in 2015 to provide specialist support for African and Caribbean heritage women affected by abuse, wrote: “Mixed feelings about yesterday’s visit to Buckingham Palace.
Responding to messages of support, Ms Fulani wrote: “Standing there in a room packed with people while this violation was taking place was so strange, especially as the event was about violence against women.
“That feeling of not knowing what to do will NEVER leave me. Almost alone in a room full of advocates.”
She said it was a “struggle to stay in a space where you were violated”.
The matter raises serious concerns for the Palace, where an unnamed member of the royal family was accused by the Duchess of Sussex last year of racism against her unborn son, Archie.