Christian Solidarity Worldwide (CSW) says Reverend Yiorvis Bravo cannot travel as the government continues to target church properties for expropriation. This is when a public body seizes a private property for a purpose they say is in the public interest.
In June he was banned from travelling outside the country because he refused to pay the government rent on a property that the authorities confiscated from him in 2013.
He received an official letter before he was due to travel to Peru to participate in a course on leadership, democracy and multimedia communications.
It said his refusal to acknowledge the government as rightful owner of his property and his failure to pay rent to the authorities has resulted in debts that prevent him leaving Cuba for any reason.
Revd Bravo did not leave the property but Housing Ministry officials offered to allow him to stay in the building if he paid US $300 per month - an amount 15 times the average annual salary in Cuba - and submitted all activities to the government in advance for approval.
Reverend Bravo refused this offer, stating he was the legal owner.
CSW says it has received numerous reports that the government has been targeting more church properties in a similar way across the country since new legislation came into effect in early 2015.
Chief Executive, Mervyn Thomas, said: "We have repeatedly raised concerns about the growing number of churches, registered and unregistered, which have been informed of the arbitrary expropriations of their properties by the government in recent months.
"The current situation of Reverend Bravo is a clear demonstration that the strategy behind these expropriations is to exert more control over religious leaders and bodies of faith.
"The expropriation of his property has been compounded by punishing him for refusing to pay an exorbitant rent to the government on property which is rightfully his.
"We continue to condemn the illegal expropriations of church properties and call on the Cuban government to rescind these orders of confiscation immediately.
"Furthermore, we call on the Cuban authorities to lift any restrictions on travel for Reverend Bravo without delay."