The government in Havana says those to be freed include inmates due for conditional release next year, as well as a number of foreign prisoners.
Those found guilty of crimes against state security will not be eligible, seemingly ruling out several high-profile political prisoners.
The Pope will make a three-day visit to the island next week.
According to Cuba's state-run newspaper Granma, prisoners were chosen for early release depending on the severity of their crimes, amount of time served, and good behaviour.
Among those to be freed are a number of inmates over 60, prisoners under 20 years old with no prior criminal records and inmates with chronic health conditions.
No prisoners with sentences for murder, other violent crimes or drug trafficking will be released, the paper said.
Pope Francis is expected to meet with Fidel Castro if the former Cuban leader's health allows.
The 78-year-old Argentine pontiff is credited with helping bring about last December's diplomatic thaw after the decades-old enmity between communist Cuba and the US.
He was directly involved in organising a series of secret diplomatic meetings between the two sides.
The Roman Catholic Church has maintained relations with Havana since the revolution and Pope Francis himself is no stranger to Cuba. He was there during Pope Benedict XVI's visit in 2012 and is the author of a book on Cuba.

Rovers took a 24th-minute lead at the Silverlake Stadium when Christian Doidge sweetly headed in Keanu Marsh-Brown's cross from the right for his 14th league goal of the season.
Eastleigh twice went close before Ayo Obileye levelled 10 minutes later, bundling in Luke Coulson's teasing corner at the back post.
Towards the end of an exciting first half, Forest Green's Dale Bennett made a fine block from Hakeem Odoffin's shot.
Eastleigh introduced newly-signed striker Darius Henderson at half-time but Rovers initially threatened most, although Ben Strevens headed just wide with 12 minutes to go amid late chances for both teams.
Report supplied by the Press Association.
Match ends, Eastleigh 1, Forest Green Rovers 1.
Second Half ends, Eastleigh 1, Forest Green Rovers 1.
Ben Strevens (Eastleigh) is shown the yellow card.
Dale Bennett (Forest Green Rovers) is shown the yellow card.
Substitution, Forest Green Rovers. Marcus Kelly replaces Keanu Marsh-Brown.
Substitution, Eastleigh. Scott Wilson replaces Hakeem Odoffin.
Substitution, Forest Green Rovers. Shamir Mullings replaces Rob Sinclair.
Substitution, Eastleigh. Jai Reason replaces Sam Togwell.
Substitution, Eastleigh. Darius Henderson replaces James Constable.
Second Half begins Eastleigh 1, Forest Green Rovers 1.
First Half ends, Eastleigh 1, Forest Green Rovers 1.
Sam Togwell (Eastleigh) is shown the yellow card.
Goal!  Eastleigh 1, Forest Green Rovers 1. Ayo Obileye (Eastleigh).
Goal!  Eastleigh 0, Forest Green Rovers 1. Christian Doidge (Forest Green Rovers).
First Half begins.
Lineups are announced and players are warming up.

The black-headed gull was unable to fly off after getting trapped about 20ft (6m) from the bank of the lake in Leicestershire.
Firefighters chipped him free from the icy water at Grove Park, Enderby, after being called by the RSPCA at about 16:50 GMT on Tuesday.
He was taken to a vet to warm up.
The gull was then taken to a nearby wildlife centre for further care before he will be released into the wild.
Firefighters used a rescue sled, which is like an inflatable raft, to reach the gull.
The RSPCA said in a statement: "He was about 20ft out on the lake and was stuck fast.
"Thankfully the the fire service came out to assist our officers and using an inflatable raft managed to reach the gull and chip him free from the ice."
Cuba has said it will release more than 3,500 prisoners in a goodwill gesture ahead of a visit by Pope Francis.
[NEXT_CONCEPT]
Forest Green missed the chance to go level on points with National League leaders Lincoln as they were held to a 1-1 draw at Eastleigh.
[NEXT_CONCEPT]
A bird that became stuck in a lake when the water froze around its feet is recovering after being rescued by firefighters.