The Nadeem Centre for the Rehabilitation of Victims of Violence, whose headquarters are in central Cairo, documents allegations of torture, death and medical negligence inside police stations and prisons.
"Two policemen... turned up today at the centre with an administrative decision from the health ministry to close" it, Aida Seif el-Dawla, one of its founders, told AFP by phone.
"The decision did not give any reasons," she said. "We managed to persuade them to postpone the closure until we went to the health ministry on Monday to understand the reasons."
A spokesman for the health ministry said the centre's closure was due to it holding "activities other than the activity allowed in its permit," but did not specify the nature of these activities.
Amnesty International said that moves to close down the centre "appear to mark an expansion of the ongoing crackdown on human rights activists in Egypt".
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Said Boumedouha, the rights group's deputy director for the Middle East and North Africa, called on Egypt to "freeze the order to close the centre and provide it with a clear explanation of the reasons behind the order."
The centre "must be given an opportunity to challenge the order before a court," he said.
It "provides a lifeline to hundreds of victims of torture and the families of people who have been subjected to enforced disappearance," he said.
"This looks to us like a barefaced attempt to shut down an organisation which has been a bastion for human rights and a thorn in the side of the authorities for more than 20 years."
Five years after police brutality sparked the revolution that toppled longtime dictator Hosni Mubarak, human rights groups are again denouncing deaths in police stations, arbitrary arrests and the disappearances of opponents of the regime.
Since the army ousted Islamist president Mohamed Morsi in 2013, authorities have launched a brutal crackdown on his supporters that has seen hundreds killed and tens of thousands jailed.
Secular activists who took part in the 2011 revolt have also been imprisoned.