Liberal Democrats Heather Kidd and Ruth Houghton say health leaders should have consulted on the closure of the unit in Union Street which chiefs say was taken because "staffing issues" have left it difficult to run.
Councillor Ruth Houghton (Bishop's Castle) said she has asked for more information on the length of time the hospital will be closed for, as "no plan or timescales have been provided."
Councillor Houghton and her colleague Councillor Heather Kidd (Chirbury and Worthen) are concerned that the need to transfer patients out of Bishop's Castle will place strains on other parts of the health service just as winter approaches.
It could also mean patients and their families from the Bishop's Castle area will have to travel many miles. The hospital website says it has 16 beds providing inpatients and outpatients services in audiology, podiatry, physiotherapy, and speech and language therapy.
It also has a palliative care suite that has received local, regional and even national recognition.
Councillor Kidd added: “Staffing has been quoted as the main reason for the closure, but not once have they raised this as an issue with scrutiny."
She added: “What has really annoyed me is this was done almost by stealth. Very few people knew what was going to happen.
“On the very day that the closure press releases were being sent out the joint health overview and scrutiny committee was meeting. An emergency item should have been tabled. I will be requesting that this is examined next time we meet."
She added: “The beds at Bishop’s Castle are usually full during the winter months and the hospital plays a key role for health care in a whole swathe of the south west of the county. Without these local beds people from southwest Shropshire will be faced with long visitor journeys and poor public transport."
She called for a plan to address recruitment issues so that the hospital can reopen quickly and provide safe care for patients and a safe working environment for staff both of which is essential.
In a statement last week Shropshire Community Health Trust, which manages the hospital, said that staffing issues over the last six months had left it "extremely difficult" to run the hospital.
A spokesman said: "Shropshire Community Health Trust (SCHT) is committed to providing high quality care, and this has proved to be extremely challenging at Bishop’s Castle due to long-standing staffing issues.
“Recruitment has been a problem for several years.
"For the last six months it has become extremely difficult to maintain the qualified staffing levels required to run the hospital.
"This has been exacerbated by the coronavirus pandemic, which has and continues to impact us severely.
“We have been actively managing the issues with our fantastic staff, but despite their best endeavours we have been unable to secure the right level of substantive staff to deliver optimum care to patients.
“We have therefore taken the difficult decision as a trust to temporarily close the hospital."
New admissions ceased at the end of the week and inpatients were to be assessed and discharged to the appropriate place of care by Sunday, October 31.
The spokesperson said they are due to start an engagement programme with the public in the winter. Its Local Care Transformation Programme, includes plans to engage, involve and "co-design new models of care with residents and communities, with a focus on prevention and promoting good health and wellbeing."
The move has been criticised by health campaigners.
Gill George, the chair of Shropshire, Telford and Wrekin Defend our NHS, said: "What lies ahead if they continue with this is a winter of crisis and people dying, avoidably, in Shropshire."