The man died after the incident around 10.30pm on Thursday.
Police say they do not believe anyone else was involved and Shrewsbury & Telford Hospital NHS Trust (SaTH), which manages the hospital, said an investigation is under way.
A spokesman for West Mercia Police said that a report had been prepared and passed to the county's coroner.
He said: "On Thursday, July 15, police attended the Royal Shrewsbury Hospital after a man had fallen from a fourth-floor window.
"The man was sadly pronounced dead.
"There is believed to be no third party involvement and a report has been prepared for the coroner."
Hayley Flavell, Director of Nursing at SaTH, said: “With deep sadness, we can confirm the death of a patient at the Royal Shrewsbury Hospital and our thoughts are with their family.
“We are working closely with the relevant authorities, as well as carrying out our own internal investigation, and cannot comment further at this time.”
West Midlands Ambulance Service said it had also attended the incident, with a crew already at the hospital going to assist.
A spokesman said: "We were called to Royal Shrewsbury Hospital at 10.35pm on Thursday, July 15, to reports of a patient who had fallen from height.
"An ambulance crew, already at the hospital, and a paramedic officer attended the scene and arrived to find a man being given CPR by hospital medics.
"Ambulance staff worked with hospital colleagues to continue resuscitation efforts whilst the patient was carried into hospital. Sadly nothing could be done to save him and he was confirmed deceased a short time later."
If you have been affected by this article contact Samaritans on 116 123 or at samaritans.org