The false alarms, the first of which occurred at the Princess Royal Hospital soon after 6am on Monday, have often meant two fire crews being despatched.
Another call-out to the Robert Jones and Agnes Hunt Orthopaedic Hospital near Oswestry at about 7am on Monday was identified as a false alarm, according to the Shropshire Fire and Rescue Service's incident log.
On Tuesday morning, two crews were sent to the Royal Shrewsbury Hospital only to find the alarm had been activated automatically and there was no danger.
Then on Wednesday morning crews from Bridgnorth and Much Wenlock were called to Bridgnorth Community Hospital to investigate another false alarm.
Two incidents were reported at the Royal Shrewsbury Hospital that afternoon, both of them without any threat identified and one found to have been caused by dust in a smoke detector.
Then this morning another two crews were sent to the Princess Royal Hospital in Telford, after what was again found to be a false alarm.
In an emergency, call the emergency services using 999. In non-emergency situations, call 101.