The Trust says the temporary closure will boost resources at Hereford County Hospital’s Accident and Emergency Department.
This will enable it to continue to see and treat patients and care for the increased number of patients requiring admission to acute hospital.
The MIUs provide treatment for less serious injuries, such as sprains, cuts and grazes and are usually open Monday to Friday.
Derek Smith, chief executive at Wye Valley NHS Trust, said: "We would like to apologise for any inconvenience this temporary closure may cause and we will re-open the Minor Injury Units as soon as possible.
“We would also like to reassure the public the safety of our patients is our priority and the decision to temporarily redeploy staff from the MIUs to the County Hospital’s A&E department was not taken lightly.
"Alternative NHS services are available locally for people requiring advice or treatment for minor injuries or illness”.
A number of other NHS services are available to local residents including community pharmacies, GP surgeries, and Asda Walk-in-Centre, Belmont Road, Hereford, open from 8am until 8pm, seven days a week.
For urgent medical help that is not life threatening the public can call NHS 111 and the A&E service remains available to anyone with a life threatening illness or injury.
Posters are being displayed at the Community Hospitals to direct the public to the other NHS facilities in Herefordshire as well as Hereford County Hospital’s Accident and Emergency department where appropriate.
Details are also published on the Trust’s website wyevalley.nhs.uk
All of the Community Hospitals' other services will continue to operate as usual.