The Duke of Sussex was filmed rapping and having a great old time with the host of The Late Late Show in the video which was released on Friday.
The Queen, who received her Covid vaccine seven weeks ago, urged her fellow Brits to get the vaccine and "think about others" rather than just themselves.
"This blurring of the lines doesn't help anyone," one senior source told the Mail Online. "When the Queen speaks like this it is her message that should be heard without other distractions. This lack of coordination is unhelpful."
Speaking of her vaccine in the video alongside medical chiefs who are overseeing the vaccine rollout in England, the Queen said, "It was very quick, and I’ve had lots of letters from people who’ve been surprised by how easy it was to get the vaccine."
She added it "didn't hurt at all" and shared how it gave her an incredible feeling of protection.
Critics suggest Harry's interview will water down the Queen's message.
Royal expert Robert Jobson told the publication, "Timing is everything isn't it. On the day that the Queen has issued a very, very important message about the whole of the nation getting the jab, that message has sort of been blurred by Harry, the man who wants a private life, talking about his private life again."
Royal expert Phil Dampier added, "As The Queen urges us to think of others, Prince Harry prances about in LA and makes the absurd claim that he hasn't walked away from the royals. What planet is he on? Hollywood I suppose."
During the interview with James Corden, Harry opened up about life with wife Meghan Markle and their son Archie, as well as their decision to quit life as working royals.
The Duke said the pressure of being in London was "destroying my mental health" and said Britain's media is "toxic".
Speaking of the couple's decision, he said, "It was never walking away. It was stepping back rather than stepping down. It was a really difficult environment, which I think a lot of people saw. So I did what any father or husband would do and thought: 'How do I get my family out of there'. But we never walked away."
The interview was shot before the Queen stripped Harry and Meghan of their royal patronages, but Harry seemed to know what was coming, saying, "My life is public service, so wherever I am in the world it's going to be the same thing. As far as I'm concerned, whatever decisions are made on that side [in Britain], I will never walk away."
Elsewhere in the interview, Harry says he has had Zoom calls with the Queen and Prince Philip and revealed Her Majesty gave Archie a waffle maker for Christmas.
He also described their son as "hysterical", sharing his first word was "crocodile".
Harry spoke of his relationship with Meghan, saying he knew she was "the one" after just two dates, adding their relationship went from "0-60 in two months".
When asked to describe a "regular night in" for the couple is like, Harry says they will make Archie's dinner, give him a bath and read him a book, before getting into bed to watch Jeopardy! or Netflix.
In the video, Harry raps to the theme tune of The Fresh Prince of Bel-Air outside the house where the show was filmed, with Corden attempting to convince him to buy it, so he can be the Prince of Bel-Air.
The pair then video call Meghan, who calls Harry 'Haz' and tells him not to buy it because she's "done moving".
Harry also gave The Crown his seal of approval, despite the Netflix show previously coming under fire for its portrayal of the royal family.
He said the show is "fictional" but is "loosely based on the truth" and captures the feeling of what is expected of the royals, who must put "duty and service above family and everything else".
"I'm way more comfortable with the Crown than I am seeing the stories written about my family or my wife, or myself, because ... that is obviously fiction, take it how you will, but this is being reported on as facts because you're supposedly news," he said.
The Duke added he'd like Homeland actor Damian Lewis to play him, should his character ever appear.
Harry and Meghan will appear in an interview with Oprah Winfrey on March 7 with the couple expected to discuss life in America.
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