The health watchdog has found that Kilcreene Regional Orthopaedic Hospital in Kilkenny, and the Midland Regional Hospital, Portlaoise, were not compliant with national screening guidelines, to protect against a serious bacterial infection called CPE.
It follows unannounced inspections of five hospitals between April and May of this year.
Following the inspections, management at the hospitals proposed measures to deal with the issues raised by the Health Information and Quality Authority.
Among the patients who must be screened for CPE are those who have been transferred from any other hospital, all admissions to critical care areas, all patients who received chemotherapy in the last year and admissions to transplant wards.
A national public health emergency plan to deal with the superbug CPE (Carbapenemase Producing Enterobacteriaceae) was announced in October last year by the Minister for Health.
The Health Service Executive issued screening guidelines to all acute hospitals in June 2017.
HIQA said that screening allows hospitals to reduce the risk of patients going on to develop CPE infection during the course of their medical treatment and to prevent the spread of it to other patients and staff.
It said that in light of the limited treatment options and substantial mortality associated with infections caused by CPE, prevention and control measures are of the utmost importance.