The Cuban Commission on Human Rights and National Reconciliation claims an operation is underway in Havana, Holguin and Santiago – cities the pontiff will visit between today and Tuesday.
The activism group says authorities have jailed “thousands of beggars, panhandlers, ragamuffins, the mentally ill and other vulnerable wanderers, most of them homeless”.
It also alleges that the operation was approved by Cuba’s highest authorities.
A statement from the commission said: “This ‘social cleansing’ intends to remove them from the view of pilgrims, foreign journalists and other visitors”.
The group has now publicly asked Pope Francis to intervene and seek the release of those picked up.
Pope Francis flies to Cuba on Saturday for a three-night visit.
His visit has sparked fears that he might speak more bluntly about democracy and human rights than the Communist government would like.
On the first papal visit to Cuba in 1998, Pope John Paul II made pointed comments about prisoners of conscience, saying they suffered “an isolation and a penalty” for merely wanting to “speak their mind with respect and tolerance”.
Pope Benedict offered far more muted remarks about general prisoners in 2012.
Cuba is sensitive to criticism of its human rights record, saying it needs to restrain critics it describes as mercenaries bent on destabilising the government.
Many of Cuba’s dissidents receive funding from US organisations, and activists are routinely detained by Cuban police for demonstrating.
In a gesture to the pope, Cuba released 3,522 prisoners last week.
But these didn’t include any of the 60 political prisoners listed by the commission.
One expert said the pope may deliver a polite rebuke by speaking in general terms.