Cancer sufferers at the Beatson West of Scotland Care Centre were forced to listen to the fire alarm, which sends out a constant beep with occasional one-second-on, one-second-off, intermittent sections, all day.
They say they were at their wits' end with the constant noise.
NHS Greater Glasgow and Clyde said the alarm was sounding as part of annual tests on the fire alarm system at the hospital.
They said they were trying to keep inconvenience to a minimum, by testing it floor by floor, throughout Wednesday and Thursday.
One patient, who has been in the hospital for 10 days and was diagnosed with leukaemia six weeks ago, said the noise started very early on Wednesday morning and continued throughout the day.
The patient, who did not wish to be named, said: "The fire alarm has been going off in here for 24 hours now.
"It is driving the staff, the doctors and nurses, and especially the patients round the twist.
"We are at our wits' end. The high pitched beep is on most of the time, sometimes it goes intermittently, but most of the time it is on all the time.
"I think we are all about to go insane here."
The Beatson is situated within Gartnavel Hospital Campus in the West End and provides care and treatment for patients with many different forms of cancer.
A spokeswoman from NHS Greater Glasgow and Clyde said: "We apologise to anyone who is inconvenienced by the noise, we are trying to keep the inconvenience to a minimum.
"But it is something we need to do to make sure our fire alarm system is fully operational."