"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".
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."
It "provides a lifeline to hundreds of victims of torture and the families of people who have been subjected to enforced disappearance," he said.
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.
Secular activists who took part in the 2011 revolt have also been imprisoned.