The pair were suspended by Kevin Blackwell on Christmas Eve following an incident at the club's official festive party last week.
"We have suspended them pending further enquiries," manager Kevin Blackwell told the Yorkshire Evening Post. "Until our internal investigation is concluded there is nothing I can say."
Oster, 26, who is on loan from Sunderland, was arrested outside a Durham nightclub two weeks ago. He was released without charge but fined by Leeds and warned about his future conduct.
The duo are set to learn their fates at a meeting on Friday.
Leeds could send Oster back to Sunderland, whilst McMaster, 22, could face a large fine and be warned about his future conduct.