South Lanarkshire Health and Social Care Partnership, in discussion with NHS Lanarkshire, took the decision to temporarily close the minor injury units last year.
The change was to further minimise the risk of patients contracting Covid-19 at both hospitals.
Due to ongoing risks linked to the well-publicised new variants, the minor injury units cannot be re-opened at this time.
Craig Cunningham, head of commissioning and performance at South Lanarkshire Health and Social Care Partnership, said: “Temporarily closing a service is not a decision that we take lightly.
“Given the frailty of many of the patients in these hospitals, the decision was taken to reduce the risk by stepping down minor injury services temporarily.
“It’s important to note that these restrictions remain in place at the current time. The minor injuries units will reopen when it is safe to do so.”
Mr Cunningham added: “We would encourage anyone requiring minor injuries services to use the services provided at University Hospital Hairmyres, University Hospital Monklands and University Hospital Wishaw.”
People with non-life threatening conditions, who think their condition is serious enough to attend A&E, should call NHS 24 (111) first – day or night.
People can still access primary care services for urgent care, including contacting their GP practice.