Patrick Grady has been named by The Herald as the MP at the centre of the claims, with his party late on Tuesday night confirming an investigation is under way.
Letters obtained by the newspaper detail concerns about his behaviour at the SNP Christmas party on December 15, 2016, at London’s Phoenix Artist Club.
It is alleged Mr Grady groped two male researchers at the party, but was being “protected” by the SNP.
The SNP has confirmed an investigation into Mr Grady has commenced.
An SNP spokesman confirmed Mr Grady, the MP for Glasgow North, had “stood aside” from his role as chief whip, adding: “The SNP has today received a formal complaint.
“That now allows due process to take placed and we will not be commenting further while an investigation is under way.”