The newspaper interviewed relatives, advisers, associates of the detainees, as well as Saudi officials, who denied the allegations.
One individual, Maj. Gen. Ali al-Qahtani of the Saudi National Guard, reportedly died in custody with "a neck that appeared twisted, a badly swollen body and other signs of abuse". France and Britain are the other two countries that he is visiting.
But he was a top aide to Prince Turki bin Abdullah, a son of the late King Abdullah and a former governor of Riyadh, and the interrogators may have been pressing the general for information about his boss, Prince Turki. The prince was expected to visit Washington, New York and Boston, a Saudi government source had told Reuters, adding that the details of the trip were yet to be finalized.
King Salman also announced that an anti-corruption conference will be held in April at which combating corruption in privatisation programs will be discussed, the Saudi government website reported.
At least 380 people were held for questioning, while 65 were held in custody at the Ritz-Carlton hotel in the capital Riyadh.
Saudi Arabia's attorney general said in January that more than $106bn was seized from the citizens arrested in the purge.
Most have since been released but they are hardly free.
To leave the Ritz, numerous detainees not only surrendered huge sums of money, but also signed over to the government control of precious real estate and shares of their companies - all outside any clear legal process.
Saudi officials said the crackdown, which came through royal decree, was in response to "exploitation by some of the weak souls who have put their own interests above the public interest, in order to illicitly accrue money".
Saudi officials did not immediately respond to AFP's request for comment, but the New York Times quoted the government rejecting the abuse claims as "completely untrue".
The former detainees were quoted by the newspaper as saying that numerous released are being forced to wear tracking devices on their ankles.
"I would guess it is about evens that there will be no global IPO", said a high-level source familiar with the preparations, saying they were proving to be a disappointment.