"Kate is furious about the larger workload. Of course she's smiling and dressing appropriately but she doesn't want this," the friend reportedly said.
"She feels exhausted and trapped. She's working as hard as a top CEO, who has to be wheeled out all the time, without the benefits of boundaries and plenty of holidays," the friend added.
The lengthy article also claimed that the Duchess of Cambridge had argued with Meghan over whether to wear tights at the Sussexes' wedding in 2018.
"There was an incident at the wedding rehearsal," the article said, quoting another friend of the Cambridges.
"It was a hot day and apparently there was a row over whether the bridesmaids should wear tights or not. Kate, following protocol, felt that they should. Meghan didn't want them to," the friend said.
But in a terse statement issued on Tuesday night, Kensington Palace said the article was full of "inaccuracies" and "misrepresentations".
"This story contains a swathe of inaccuracies and false misrepresentations which were not put to Kensington Palace prior to publication," it said.
The statement did not point to any of the magazine's claims in particular.
It is extremely rare for palace officials to slap down claims made about the royal family in the media.
ITV News's royal editor Chris Ship described it as an "unusual step" that proved Kensington Palace was "clearly very unhappy".
The Duke and Duchess of Cambridge have kept busy during the coronavirus lockdown, conducting several official royal duties via video link.
They played bingo with residents of a care home in Wales last week, while earlier this month they joined a video call with volunteers from a mental health text service.
Harry and Meghan, who dramatically quit the royal family a year after they got married, have also kept busy in the United States.
The two spent Easter delivering meals for those too ill to cook for themselves and helped to provide 250,000 meals for struggling Brits during lockdown with their $166,000 wedding donation.
