Apparently, the Queen also feared any photos of her and her great-granddaughter would be shared with US TV networks, the publication reports.
The Queen met Lilibet for the first time on Thursday last week at Windsor Castle, with Harry and Meghan denying their personal photographer the special moment.
"Harry and Meghan wanted their photographer to capture the moment Lilibet met the Queen," a source told The Sun.
"But they were told no chance. It was a private family meeting."
Investigative journalist Tom Bower, who is working on a biography about Meghan, told the Daily Mail: "Meghan must have been furious when she heard that photographs of their Windsor meeting were forbidden."
"Banned from the balcony for Trooping the Colour, no shot of her with the Queen in St Paul's and then the final blow was no shot of Lilibet with her great-grandmother. Finally, the Palace is playing a good hand."
He added, "The Sussexes’ contract with Netflix is in jeopardy. The veto of photos will fuel the Sussexes’ resentment. Harry’s reprisal could be more revelations in his book billed to be published later this year. This is a dangerous game for both sides."
The pair celebrated Lilibet's first birthday at their former home Frogmore Cottage on Saturday, releasing their first solo photo of the tot to mark the occasion.
Zara and Mike Tindall's children Mia, eight, Lena, three, and Lucas, one, were expected to attend the party, along with Peter Phillips and Autumn Kelly's daughters Savannah, 11, and Isla, 10.
Harry and Meghan did invite Prince William, Kate Middleton and their three children to the party as an 'olive branch' but the Cambridge's didn't attend, Page Six reports.
A source told the US publication that things between the brothers are "still fraught" and that "William is still wary of spending any time alone with Harry as you never quite know what may be reported back afterwards".
William and Kate took their children to Cardiff Castle to celebrate the Jubilee instead.
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