Karim Wade served three years of a six-year sentence for illegally enriching himself during his father's rule.
He left Senegal immediately after his release for Qatar, a justice ministry spokesman said.
Karim Wade was charged with corruption after President Macky Sall took power in elections in 2012.
He defeated Abdoulaye Wade and pledged to tackle corruption.
Karim Wade was also fined $230m (Â£150m) for illegally accumulating a fortune of at least $200m.
He had hidden away funds in offshore companies in the British Virgin Islands and Panama, a court ruled.
The payment of the fine was not covered by the pardon, Mr Sall's office said in a statement.
The BBC's Maud Jullien reports from the capital, Dakar, that Mr Sall freed Karim Wade following pressure from influential religious leaders who felt the move would enhance national unity in the West African state.
The opposition Senegalese Democratic Party chose Karim Wade as its presidential candidate for the 2019 polls while he was in prison.
It is unclear whether he is still eligible to run for the presidency.
Karim Wade was a senior minister in his father's government, and was in charge of major infrastructure and energy projects.
His large portfolio led to him being dubbed "the minister of the earth and the sky".
The son of Senegal's ex-President Abdoulaye Wade has been freed from prison after receiving a presidential pardon, the government has said.