A hospital emailed dispensers are being stolen every day, with some grabbed from the end of patients' beds.
The email said: "I have had discussions today with [the procurement team] about the potential future shortage of the 400ml foaming hand sanitiser pumps that go on the ends of beds and on trolleys.
"Unfortunately, relatives seem to be taking them from the ends of beds.
"Whilst we acknowledge that there is potential for a national shortage of foam due to the coronavirus, we do not want our patients to be put at risk of other infections whilst they are in hospital."
Wards are being ordered to halve the number of hand sanitisers in a bid to ration the bottles for the future.
The thefts have sparked vicious backlash on social media, with one patient revealing her struggle while in the cancer ward.
"Absolutely disgusting. I'm a cancer patient just starting chemo and can't find any hand sanitiser anywhere but stooping this low and stealing from the very vulnerable is beyond a joke," the woman said.
Others called them "selfish', while another wrote: "Not sure these people that are stealing it realise that to stop the spreading everyone needs to clean their hands not just them."
A spokeswoman for the hospital has said that "Nothing like this has ever happened in all the years we've had the gel."