"The total blanket of secrecy over the matter makes it another one of those underhand deals which in the past have given Pakistan its worst moments of shame and whose consequences are never thought out," it said.
Mr Sharif arrived in Saudi Arabia on Sunday, accompanied by his father, Mian Mohammad Sharif, his jailed brother, Shahbaz Sharif, wife Kulsoom Nawaz and 15 other close relatives.
After his overthrow in a coup last year, he was sentenced to life imprisonment on hijacking and terrorism charges.
But his prison terms have now been commuted by the military government.
Lack of accountability
The daily News denounced the move in a strongly-worded editorial on Monday.
"The total blanket of secrecy over the matter makes it another one of those underhand deals which in the past have given Pakistan its worst moments of shame and whose consequences are never thought out," it said.
Dawn newspaper said the military government was supposed to be committed to accountability.
"But the Sharifs have been allowed to go when many cases against them have yet to be settled."
There was reported to be a mixed reaction from political leaders.
But the move was denounced by the Pakistan People's Party of Benazir Bhutto and the main Islamist party, the Jamaat-e Islami.
Popular reaction was also reported to be hostile.
"You let Nawaz Sharif go, who is a big fish, with truckloads of luggage, and then you keep his aides and other businessmen in jail?" one man was quoted as saying by Associated Press.
However, the US Government has welcomed the development, and praised Saudi Arabia for working out an arrangement with the Pakistani authorities.
Assets seized
The government says it has confiscated bank deposits worth 300m Rupees ($5m), as well as five industrial properties, five residential plots and 24 hectares (60 acres) of agriculture land.
But despite the seizure of some their property, the Sharifs were allowed to take 22 containers packed with household goods, including carpets and furniture.
Mr Sharif's family say he has had to go abroad for urgent medical treatment for a cardiac disorder.
His son Hasan, said: "Heart disease is common in my family. When my father was in jail he had a lot of anxiety. Problems were bound to happen," said his son Hasan.
'We will return'
Mrs Nawaz held out the hope of returning to Pakistan in the future.
"It is our country. Nobody can turn us out. If we go out for medical treatment we will return," she said.
Mr Sharif remains head of the former ruling party, the Pakistan Muslim League, although he appointed close aide Javed Hashmi as acting president in his absence.
A 21-year ban on holding public office, imposed on Mr Sharif at his trial, remains in force.
A Saudi diplomatic source said that Mr Sharif would not be allowed to take part in political activity while he was living there.
Saudi officials said Mr Sharif would perform umra, a minor Muslim pilgrimage to Mecca, before being admitted to hospital for treatment.
The BBC Islamabad correspondent says that Mr Sharif's exile removes a major opposition figure from the country prior to elections due before the end of 2002.