The 22-year-old, who can play full-back or wing and has three caps, appeared at Edinburgh Sheriff Court on Wednesday where his sentence was deferred following a guilty plea.
McLean, a former pupil of Merchiston Castle School in Edinburgh, scored two tries on his Scotland debut against Tonga in October 2021. He joined Glasgow in 2020 after graduating from the FOSROC Scottish Rugby Academy. His last club appearance came in the win over Perpignan on December 16.
A Glasgow Warriors statement read: "Rufus McLean is suspended for all club activity and is unavailable for selection following a guilty plea to charges under the Domestic Abuse (Scotland) Act 2018 in December 2022.
"Glasgow Warriors does not condone abuse of any kind and therefore, along with Scottish Rugby, immediately suspended the player following his plea.
"An internal investigation has been instigated and a disciplinary hearing will be held this week.
"Legal proceedings in this matter are not concluded therefore no further comment will be made at this time."