The Minor Injury Unit at Monnow Vale Health and Social Care Facility closed last Monday (28th November).
The closure comes after a Health Board review found many patients had inappropriately attended the unit for care after surgery and for primary care services.
The units at Chepstow Hospital and County Hospital in Pontypool also closed.
Other services at these sites remain unaffected.
Patients will now be supported to access this care through hospital or community clinics and their GP's surgery.
Extra community clinic arrangements were introduced from 21st November 2011 to ensure alternative services are in place.
Patients who require urgent medical attention for a true minor injury should now go to the Royal Gwent Hospital, Nevill Hall Hospital, Ysybyty Aneurin Bevan or Ysybyty Ystrad Fawr in Ystrad Mynach.