The 71-year-old woman was attacked at the Queen Elizabeth University Hospital on Thursday.
The incident was reported to police by hospital staff.
A spokesman for NHS Greater Glasgow and Clyde said: “We can confirm an incident took place involving two patients, which our staff reported to the police.
“This is now a police matter.”
A Police Scotland spokeswoman said: “Police Scotland officers have received a report of a 71-year-old female patient being sexually assaulted within the Queen Elizabeth Hospital on Thursday.
“Inquiries are currently ongoing.”