Monastery
late Middle English: via ecclesiastical Latin from ecclesiastical Greek monastērion, from monazein ‘live alone’, from monos ‘alone’.
wiktionary
From Middle English monasterie, from Old French monastere, from Latin monastērium, from Ancient Greek μοναστήριον(monastḗrion, “hermit's cell”), from μόνος(mónos, “alone”). Doublet of minster.
etymonline
monastery (n.)
"place of residence occupied in common by persons seeking religious seclusion from the world," c. 1400, monasterie, from Old French monastere "monastery" (14c.) and directly from Late Latin monasterium, from Ecclesiastical Greek monastērion "a monastery," from monazein "to live alone," from monos "alone" (from PIE root *men- (4) "small, isolated"). With suffix -terion "place for (doing something)." Originally applied to houses of any religious order, male or female, but commonly especially one used by monks. Related: Monasterial (mid-15c.).