Tallaght Hospital has confirmed that a patient refused care from two consultants on the grounds of religion.
The woman turned down treatment from a female consultant who was wearing a hijab. The patient asked her if she was Muslim, and when she said she was, the woman asked for another medical professional to look after instead.
The issue came to light when the patient's daughter allegedly wrote about her mother's experience on social media.
She reportedly claimed that a second consultant, who was also Muslim, entered the room and her mother then asked for a "non-Muslim consultant".
The social media post also said that the woman did not want a Muslim doctor involved in her medical care.
Independent councillor Dermot Looney took to Twitter to say that Muslim doctors do "amazing work" around Ireland and in Tallaght.
The hospital confirmed that a patient had refused treatment.
"Tallaght Hospital cannot comment on individual cases due to patient confidentiality," said a spokesman.
"However, our hospital's values emphasise respect, and the hospital's establishing charter guarantees the free profession and practice of religion by all associated with the hospital and in particular the members of staff.
"These values are upheld by all staff, and the hospital expects patients to respect these values of fairness and equity."
Tallaght Hospital has since confirmed that treatment was provided to the woman in question as the hospital has a duty of care to all its patients.
A spokeswoman for the Muslim Association of Ireland said she feared that acts carried out by groups such as the so-called Islamic State were turning people against all Muslims.
"We do not know why this patient reacted the way she did, but we fear Muslims are facing racism from members of society who wrongly believe that such terror groups are acting in the name of Islam," said the spokeswoman.
"We are the first victims of these terror groups and then everyone turns against us because they think we are all the same and that the killings are done in our name.
"Sometimes these attitudes happen through ignorance, but it fuels racism.
"What I would say to this patient is read more about Islam and ask the doctors' colleagues about them before judging them."