Judge Andrew McFarlane said he accepted as proved a series of allegations made by Mohammed's former wife, Princess Haya bint al-Hussein, 45, half-sister of Jordan's King Abdullah, during a custody battle over their two children at London's High Court.
Haya fled to London on April 15 last year with the children, Jalila, 12, and Zayed, 8, fearing for her safety amid suspicions that she had had an affair with one of her British bodyguards.
As part of the ensuing custody case, Andrew McFarlane, President of the Family Court division in England and Wales, made a series of "findings of fact" about allegations raised by Haya during hearings over the last nine months.
McFarlane said he accepted her claim that Mohammed arranged for his daughter Shamsa, then aged 18, to be kidnapped off the streets of Cambridge in central England in 2000, and had her flown back to Dubai.
He also ruled it was proved that the sheikh had arranged for Shamsa's younger sister Latifa to be snatched from a boat in international waters off India by Indian forces in 2018 and returned to the emirate in what was her second failed escape attempt.
Both remained there "deprived of their liberty", McFarlane said.
In the judgements published on Thursday, McFarlane accepted that the sheikh subjected Haya to a campaign of intimidation which made her fear for her life.
He said the sheikh, who married Haya in 2004, had divorced her on the 20th anniversary of the death of her father King Hussein of Jordan, timing she said was deliberate.
"I have ... concluded that, save for some limited exceptions, the mother has proved her case with respect to the factual allegations she has made," McFarlane said.
The sheikh, 70, vice-president and prime minister of the United Arab Emirates, did not appear himself during the court case and instructed his lawyers not to put forward a challenge to the claims, which his lawyers said he rejected.
The judge's conclusions were made in December but could only be reported after restrictions were lifted on Thursday after the UK Supreme Court earlier rejected Mohammed's request for permission to appeal against their publication.
McFarlane said the allegations made by Haya about the abduction and torture of Shamsa and Latifa and the threats made against her were proved, with the exception of her claim that an arranged marriage was being sought between Jalila and Saudi's Crown Prince Mohammed bin Salman.
Last July, the judge had issued a temporary forced marriage protection order in respect of Jalila over Haya's fears but said these were only based on hearsay evidence.
"The allegations that the father ordered and orchestrated the kidnap and rendition to Dubai of his daughters Shamsa and Latifa are of a very high order of seriousness," said McFarlane.
"They may well involve findings, albeit on the civil standard, of behaviour which is contrary to the criminal law of England and Wales, international law, international maritime law, and internationally accepted human rights norms."
McFarlane said the sheikh had denied all the allegations, but said of his account relating to Shamsa and Latifa that "he has not been open and honest with the court".
"I have found that the father acted as he did with respect to Shamsa and Latifa, and I have found that he continues to maintain a regime whereby both of these two young women are deprived of their liberty, albeit within family accommodation in Dubai," he said.