A police report on the closure of the church in Zager, which was obtained by Christian persecution charity, Open Doors states: "The nuns were told to leave the hospital immediately and were prevented from taking hospital equipment with them."
The incident follows a number of sources claiming nuns in health facilities have faced evictions recently and have been left to "fend for themselves".
Last month, the new UN Special Rapporteur on the situation of human rights in Eritrea, Daniela Kravetz, stated that during the closures, soldiers were posted outside Catholic health facilities, patients were ordered to go home, and health staff were threatened.
She explained: "The seizure of these health facilities will negatively impact the right to health of the affected populations, in particular those in remote rural areas.
"By curtailing the activities of the Catholic Church, the Eritrean authorities are restricting the right of their citizens to enjoy quality health care."
In May, 2002, Eritrea outlawed Christian denominations not affiliated with the Catholic, Evangelical Lutheran or Orthodox Christian Church or and Sunni Islam, and began shutting down Evangelical and Pentecostal churches.
Christians who worship in unregistered churches can face punishment and any believers in the armed services caught practicing can be imprisoned.
The government has insisted that the closures are in line with regulations introduced in 1995 that ban religious institutions from involvement in programmes with schools, hospitals, agriculture and the elderly.
Eritrea is number seven on the Open Doors World Watch List, which ranks where Christians face the most persecution. The East African nation is often referred to as the North Korea of Africa.
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