Cuban security forces arrived at Pastor Esmir Torreblanca's house at 6am.
He, his wife and their two children - both under the age of eight - were sleeping.
The officers then bulldozed the house, which also served as a church, to the ground.
When another Cuban pastor, Rev Lleonart Barroso, went to console Pastor Esmir and his family, he was summoned to court under threat of arrest.
There, the Cuban government tried to force Rev Barroso to sign a document that could be used by officials as a reason to arrest him again in the future. He refused to do so.
Rev Barosso said: "I intend to continue on with my activities in the defence of religious freedom in Cuba."
Mervyn Thomas, chief executive of Christian Solidarity Worldwide, told Premier: "Once again we call on the Cuban government to cease its harassment of Rev Lleonart Barroso.
"We are deeply concerned that the Cuban government appears to equate the defence of freedom of religion or belief with 'counter-revolutionary' activity, even as it publicly maintains that these fundamental rights are respected in Cuba.
"CSW reminds the Cuban government of the provisions in the ICCPR and the ICESCR, which it has signed, to protect and uphold religious freedom and the civil rights of its population.
"We urge members of the international community to make representations to the Cuban government in support of Rev Lleonart Barroso, and to hold the Cuban government to account for its continued violations of religious freedom."
CSW says the church of another Cuban minister, Pastor Yiorvis Denis, has also received several threats of church closure and confiscation of property.