Ms Fulani likened the conversation with the 83-year-old Lady Hussey to "an interrogation".
A black British charity boss who was repeatedly asked where she was "really" from at a royal reception says the encounter was an "abuse".
Ngozi Fulani was questioned about her background by Prince William's godmother, Lady Susan Hussey at Buckingham Palace on Tuesday.
The late Queen's lady-in-waiting has since resigned.
Ms Fulani likened the conversation with the 83-year-old Lady Hussey to "an interrogation".
The palace described the remarks as "unacceptable and deeply regrettable".