Bosses at the hospital are in the process of contacting 65 patients who may also be affected after being on the same ward as a person found to have the condition.
Other staff are also being monitored for signs of scabies after it was discovered on Gate 21, the haematology day unit at the Aberford Road Hospital.
Martin Barkley, chief executive of Mid Yorkshire Hospitals NHS Trust, said: “We had a patient in who we then discovered to have scabies, which is a highly infectious condition.
“We are contacting other patients who may have had contact, not necessarily with the patient but who had been in the same vicinity or touched things that patient touched.
“We are in process of contacting patients that we think might have been at risk of contracting the irritating skin condition.
“At the moment we only know that one other patient has been affected. We are talking to staff as well.”
Scabies causes intense itching which is usually worse at night and skin rashes.
The condition is caused by mites which can be transmitted between people by physical contact.
It can also be passed on by coming into contact with contaminated towels, clothing or bed sheets, although this is less common.
NHS guidance says scabies infestations can spread quickly because people are usually unaware they have the condition until two to three weeks after the initial infection.
Mr Barkley said: “It is highly contagious but easily treatable. It’s an inconvenience for people as much as anything else.”
A trust spokeswoman added: “The original case of scabies was admitted to Gate 21 from August 26.
“Gate 21 is currently on restricted visiting. We restricted transfers of patients from ward 21 to other wards and departments and to care homes.”