Islam explicitly forbids monasticism, so there are no Islamic monasteries. Perhaps you are thinking of Muslim centers of worship, which are called Mosque in English and Masjid and Jame'a in Arabic, or Islamic Schools, which are called Madrassas.
It is called Masjid.
An Abbot or Archimandrite in a male monastery, and an Abbess or Mother Superior in a female monastery or convent.
Monastery for monks (males).Nunnery or convent for nuns (females).
it is called an abbacy
oblate
An abbot is the leader of a Monastery. IF the leader was a woman, she was called the abbess.
vihar
Monastery
monastery, priory
A monastery or it sometimes is called a convent.
priory
Men: AbbotWomen: AbbessKnown as an abbot or translated as such.
There were a group of French monks who had started a new monastery in the town of Cluny. They followed a strict schedule of prayers and religious services. The monastery was called the Cluny Monastery.