The Canadian stylist wrote on Instagram: "3 years of undeserved hate and abuse. It's enough."
Her words were taken as referring to the duchess, who along with the Duke of Sussex, has been under the spotlight for taking four private jet journeys in 11 days, despite their environmental campaigning.
Mulroney posted a quote, which read: "When someone faces unfair criticism, you call it out.
"When that person is your friend and your family, you call those critics what they truly are. Shame on you, you racist bullies."
Mulroney was among the confidantes who supported Meghan in the run up to the royal wedding, when the former Suits star's father Thomas Markle pulled out of attending.
Meghan, who began dating Harry in 2016, is the first mixed race person in modern history to marry a senior British royal.
Her father is of Dutch and Irish descent, and her mother, Doria Ragland, is African-American.
Author Matt Haig compared Meghan's treatment in the media to that of Harry's late mother Diana, Princess of Wales when she was dating Dodi Fayed.
"Anyone old enough to remember the viciousness of the journalists who went after Diana in the months before she died, for daring to fall in love with a Muslim, must find the Harry and
Meghan coverage a rather sinister deja vu," he wrote on Twitter.
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Celebrities including singer Sir Elton John, pop star Pink and chat show host Ellen DeGeneres have all publicly defended Harry and Meghan.
Sir Elton revealed he provided Harry and Meghan and their baby son Archie with a private flight to Nice to "maintain a high level of much-needed protection".
He condemned the "relentless and untrue assassinations on their character" and wrote on social media that he had made sure the flight was carbon neutral by making the "appropriate contribution" to a carbon footprint fund.
The Sussexes' trip to Nice followed a reported holiday to Ibiza to mark the duchess's 38th birthday earlier this month.
Pink said the duchess has been subjected to "the most public form of bullying I have seen in a while" and called on people to show "it's cool to be kind", while DeGeneres said the royals were "the most down-to-earth, compassionate people".
Greenpeace UK's chief scientist Dr Doug Parr warned that carbon offsetting was "not a meaningful response to aviation emissions".
He added on Twitter: "Good works CAN be done with cash out into offset schemes, but it is no solution."