The official Communist Party daily Granma published the decision by the Council of State to free 3,522 prisoners "on the occasion of the visit of His Holiness Pope Francis."
The Argentine-born pope is visiting Cuba September 19-22, the first stop on a trip that also will take him to the United States.
In Cuba, he will visit Havana, the northeastern city of Holguin and Santiago de Cuba on the southeastern end of the island. He is expected to meet privately with President Raul Castro.
The Catholic Church is the sole independent institution allowed to function in the country, and it has emerged as a key intermediary in the island's transition to a post-Castro era.
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With the church's encouragement, Raul Castro has pressed a gradual opening of Cuba's economy while maintaining strict Communist Party control over its political system.
In return for its support, the church has been given greater access to the state media, and is allowed to distribute its publications within the island. In 2010, it opened its first seminary in Cuba in half a century.
The prisoners -- a wide range that includes the ill, the aged, the very young, women and foreigners -- will be released within 72 hours, Granma said.
They were selected "by the nature of the acts for which they were jailed, their behavior in prison, the time of punishment and health concerns," Granma said.
Except in a few "humanitarian" cases, prisoners convicted of murder, rape, pedophilia, drug trafficking, violent crimes or crimes against the state will remain behind bars.
In 2012, the last year for which government statistics have been made public, there were an estimated 57,000 inmates in 200 prisons around the island.