An associate of the Queen's daughter told the Sunday Telegraph: "She is very upset and angry."
The paper said Tindall's roistering rugby behaviour had come under fire with the royal family before - when the couple married eight weeks ago.
Tensions reportedly arose before the wedding day about the boisterous behaviour of his rugby team-mates at the royal reception. Fellow England player, Iain Balshaw, was told to submit a draft of his best man's speech to the Palace to be vetted for any inappropriate language.
Evidently, copious amounts of drinking was allowed, with one guest describing the nuptials as more of a boozy knees-up than a regal celebration.
"There was a lot of drinking. In fact, make that a hell of a lot of drinking."
Tindall was still in his morning suit the following morning.
It's not the first time Princess Anne has voiced her displeasure about Tindall. England's rugby captain told a sports show producer in March his royal mother-in-law-to-be had asked him to have corrective surgery on his nose before he married her daughter because she was worried about how the wedding photos might look.
The 32-year-old rugby player has broken his nose eight times in his rugby career, but says he is unlikely to go under the knife again after having corrective nasal surgery years ago.
Brendan Cole's late-night dance with Princess Eugenie
While Zara raced to New Zealand to have a showdown with her wayward hubby after he was caught boob-diving an anonymous blonde, another of the Queen's granddaughters, Princess Eugenie, was busy making headlines in the UK with a New Zealander.
Christchurch-born Brendan Cole, a professional dancer on the UK reality series Strictly Come Dancing, "won over" the 21-year-old daughter of the Duke and Duchess of York, the Telegraph reported.
At the relaunch of London's trendy Cuckoo Club in Mayfair last week, Cole took to the floor with the young royal "for a lively dance as [electronic dance duo] Basement Jaxx performed".
Eugenie's sister Princess Beatrice was there with Prince Harry's ex-girlfriend Florence ("Flee) Brudenell-Bruce, and Ronnie Wood's ex-wife Jo - Cole's former dance partner on Strictly.