Staff at The Robert Jones and Agnes Hunt Orthopaedic Hospital (RJAH), near Oswestry, say it is "unacceptable" and is putting patients and staff at risk.
The trust says only a small minority of people are stealing the items, which have been in short supply, but warned that it is impacting on those who need them the most.
Posting on Twitter, the trust said: "Regrettably we are seeing thefts of our hand sanitisers and toilet roll at RJAH.
"This is unacceptable and is putting our patients and staff at risk.
"We understand there have been shortages of these items in shops but taking them from hospitals impacts those who need them most. Don’t be a #COVIDIOT.
"Thankfully, these incidents refer to a small minority of individuals.
"A big thanks to those of you, who have gone out of your way to show us kindness and offer your support. It really is appreciated."