It was confirmed that Piers had quit the ITV breakfast show on Tuesday.
His departure came after it was revealed he is being investigated by TV watchdog Ofcom after the organisation received more than 41,000 complaints about his remarks on Monday's show.
WATCH: Piers Morgan storms off GMB set halfway through show
According to PA, it's understood that Meghan's concern was not about the personal attacks on the validity of her racism allegation made against the royal family, nor her claims she was not supported by the institution when experiencing suicidal thoughts.
The complaint is understood to focus on how Piers' comments may affect the issue of mental health generally and those attempting to deal with their own problems.
Piers was also criticised by mental health charity Mind, who said in a tweet it was "disappointed and concerned" by his comments.
The organisation added: "It’s vital that, when people reach out for support or share their experiences of ill mental health, they are treated with dignity, respect and empathy."
Piers will not be returning to Good Morning Britain
Buckingham Palace released a statement on Tuesday night in response to Harry and Meghan's interview, in which the Duchess had also claimed that Prince Harry told her about a conversation with a family member where there were "concerns" over Archie's skin tone when he was born.
The statement on behalf of the Queen read: "The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan.
"The issues raised, particularly that of race, are concerning. While some recollections may vary, they are taken very seriously and will be addressed by the family privately.
"Harry, Meghan and Archie will always be much loved family members."
Make sure you never miss a ROYAL story! Sign up to our newsletter to get all of our celebrity, royal and lifestyle news delivered directly to your inbox.