The Duchess of Cambridge's sister took civil court action against a "person or persons unknown" after her account was said to have been hacked.
The Sun reported it was offered the images, which included shots of Prince George and Princess Charlotte.
A 35-year-old man was arrested on suspicion of an offence under the Computer Misuse Act and later bailed.
The allegations emerged after private pictures were said to have been offered to the newspaper via encrypted messaging service WhatsApp.
The Sun said it had been approached by someone using a pseudonym and asking for Â£50,000 within 48 hours.
Barrister Adam Wolanski, who led Miss Middleton's legal team, said she thought there had been a "genuine hack".
He said it was a "flagrant" and "criminal" act which had caused Miss Middleton "considerable distress".
Police said they were investigating the allegations and a 35-year-old man had been released on police bail pending further inquiries. He was arrested at an address in Northamptonshire late on Saturday.
In the summer, Miss Middleton and hedge fund manager James Matthews confirmed their engagement, with a wedding planned for next year.
Several high-profile figures have had images stolen from their iCloud accounts, including actress Jennifer Lawrence and singer Rihanna.
In July, American Edward Majerczyk pleaded guilty to running a phishing campaign to steal private pictures and videos from film and TV stars, in what was known as the "celebgate" affair.

Matthew Daley, 35, killed Donald Lock, on the A24 in Findon, near Worthing, last July after the 79-year-old ran into the back of his vehicle.
He was convicted of manslaughter after he admitted stabbing Mr Lock to death, claiming diminished responsibility.
Daley was told he would initially serve his time in a secure mental hospital.
Lewes Crown Court heard Daley was a paranoid schizophrenic whose mother, Lynda, had pleaded with mental health experts to have him sectioned.
She told the court the day she heard Mr Lock had been killed was "the day that all your nightmares came true".
Daley was charged with murder, but never denied killing Mr Lock on 16 July last year.
Daley will be held in Hellingly medium-secure psychiatric hospital in East Sussex under the Mental Health Act.
Should his health improve, he will then be transferred to prison.
Mr Justice Singh said the killing was a "violent, unprovoked attack" in front of members of the public, aggravated partly by Mr Lock's age and the use of a weapon.
"It's clear from the verdict that the defendant's responsibility for the homicide was substantially impaired," he said.
"It does not follow that it was completely extinguished."
Prior to the start of the trial, Sussex Partnership NHS Foundation Trust apologised for not doing more.
It has since announced an independent review into 10 killings involving patients known to the Trust, including the case of Matthew Daley.
Mr Lock's son Andrew said the sentencing of Daley did not did not remove from the family's memories the horror of what happened.
"However, at least we can move on knowing that the public are properly protected from a man who, whilst badly treated by the NHS by a catalogue of failures, is a danger to the public if not properly supervised and medicated," he said.
"It is important to note Mr Justice Singh's observation this was not a public inquiry into the failings of the NHS.
"But it is now up to the NHS that the systematic arrogance that exists in the medical world changes for good and that they wake up to the fact that we all deserve to be listened to."

The crash happened at about 14:15 BST on the B1191 at Thornton, near Woodhall Spa.
Lincolnshire Police said the motorcyclist killed in the collision lived locally, but has not released any further details. The tractor driver was not injured.
The force has appealed for witnesses to the collision to come forward.
The B1191 was closed in both directions between the B1192 Tattershall Road junction in Woodhall Spa and the A158 Jubilee Way junction in Horncastle
The High Court has banned publication of photographs allegedly stolen from Pippa Middleton's iCloud account.
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A man who stabbed a retired solicitor 39 times after a crash between their cars has been given life and will serve at least 10 years.
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A man has died in a collision between a tractor and a motorcycle in Lincolnshire.