Mid Yorkshire Health Trust, which runs Dewsbury District Hospital, has said the beds of "very ill" patients could be turned towards the holy city if requested and if it was practical to do so.
Today, Coun Khizar Iqbal (Con, Dewbsury South), executive member for community cohesion in Kirklees, said: "It's bonkers.
"When I first heard this I couldn't believe it. I have spoken with religious leaders and they have told me there is no requirement for beds to be turned. I do not know why this has come up.
"Once again, the Muslim community is being highlighted in a negative way."
Coun Iqbal, a practising Muslim, went on: "Members of the Muslim community are perfectly happy with the care offered at Dewsbury Hospital.
"It's not practical. There is a lot of medical equipment attached to beds. Hospitals should be there for medical care. No one I know of has ever complained about this."
Coun Iqbal said he would be seeking an urgent meeting with hospital managers. "It's important we work together with the hospital so we do not have these politically correct incidents."
Hospital managers at the Mid Yorkshire NHS Trust have tried to play down the planned changes, which also included providing running water for Muslim patients to wash before and after praying and halal food.
But their original press release highlighted the changes and quoted nurse Beverley Brook from Ward 6, who said: "This gave me a greater understanding on how we can make small changes that will really make a difference to our Muslim patients. I'll be taking everything that I learnt back to my colleagues on the ward."
Managers at the trust, which also runs Pinderfields and Pontefract hospitals, denied nurses had not been "told" to move the beds of Muslim patients, adding it would be up to their discretion and only done if the family of the patient requested it.
Julia Squire, chief executive of the trust, said some Press reporting had been incorrect. "Let me be absolutely clear: no employee has been or will be ordered to turn hospital beds to face Mecca five times a day."
Dewsbury Labour MP Shahid Malik said: "The trust, in its role as the final carer for terminally ill patients, was merely looking at ways of making their last days of life as comfortable as possible and are well-intentioned."