Meghan, whose mother is Black and father is white, said she was naive before she married into the royal family in 2018, but that she ended up having suicidal thoughts and considering self harm after asking for help but getting none.
"They didn't want him to be a prince or princess, not knowing what the gender would be, which would be different from protocol, and that he wasn't going to receive security," Meghan said in an interview with Oprah Winfrey aired on CBS late on Sunday.
"In those months when I was pregnant, all around this same time, so we have in tandem the conversation of, 'you won't be given security, not gonna be given a title' and also concerns and conversations about how dark his skin might be when he's born."
She declined to say who had aired such concerns. Asked if she was silent or had been silenced, she replied: "The latter."
The highly anticipated interview is set to intensify an already acrimonious row between Meghan and Harry on one side and the British monarchy on the other.
The couple have stepped down from their royal duties and are starting a new life in the United States.
Harry said he left because of a lack of understanding and because he was worried about history repeating itself - a reference to the 1997 death of his mother Diana.
He said he had not blindsided his grandmother, the queen, as he had too much respect for her, although his father, Prince Charles, had stopped taking his calls.
"I had three conversations with my grandmother, and two conversations with my father before he stopped taking my calls. And then he said, can you put this all in writing?" Harry said.
Their detractors say the couple want the glamour of their positions without the dedication it requires or scrutiny it brings.
To their supporters, their treatment shows how an outdated British institution has lashed out against a modern, biracial woman, with undertones of racism.
'QUEEN HAS BEEN WONDERFUL'
There have also been allegations of bullying against Meghan which first appeared in The Times newspaper in the buildup to the couple's appearance.
Buckingham Palace, which has made no comment so far on the interview, said it would investigate the claims, adding it was "very concerned."
In response to the report, a spokeswoman for Meghan said she was "saddened by this latest attack on her character, particularly as someone who has been the target of bullying herself."
Meghan told Winfrey that people within the royal institution not only failed to protect her against malicious claims but lied to protect others.
"It was only once we were married and everything started to really worsen that I came to understand that not only was I not being protected but that they were willing to lie to protect other members of the family," Meghan said.
"There's the family, and then there's the people that are running the institution, those are two separate things and it's important to be able to compartmentalise that because the queen, for example, has always been wonderful to me."
Meghan denied a newspaper story that she had made Kate, Duchess of Cambridge, cry before the wedding and said it was a turning point in her relations with the media.
"That was a turning point," Meghan said. Asked if she made Kate cry, Meghan replied: "The reverse happened."
"A few days before the wedding she (Kate) was upset about something, pertaining to yes the issue was correct about the flower girl dresses, and it made me cry. And it really hurt my feelings."
Meghan said she had been naive before her wedding and did not realise what she was marrying into when she joined the British royal family.
"I will say I went into it naively, because I didn't grow up knowing much about the royal family," Meghan said.
Meghan explained that she was not being paid for the interview.