The radiographer was told by managers at the Royal Berkshire Hospital in Reading that she must either follow the national dress code designed to combat superbugs and roll her sleeves up, or leave.
The command militated against her religious beliefs. Islamic women are supposed to dress modestly and cover their bodies while in public.
The woman, who has worked as a therapeutic radiographer for 10 years, has described her situation as a "continuous nightmare" and says she has been "emotionally torn about" over losing her job.
She admitted that she might not be able to get another job, but has no regrets. She has vowed to campaign against the NHS's "bare below the elbows" policy.
The hospital claims she initially complied with it and said it was "surprised" when weeks later she told managers that she could not abide by with the rules.
After a meeting with her bosses on August 1 she was given an ultimatum and chose to leave her post, writes Martin Beckford in Telegraph newspaper.
Clare Edmondson, Director of Human Resources for the Royal Berkshire NHS Foundation Trust, said: "When she voiced her objection, she accepted the opportunity to meet with the Trust Chaplain and we also offered her the opportunity to meet with an Imam to discuss her concerns, but this was declined.
"The Trust Chaplain and Imam both stand behind our 'bare below the elbows policy' and support the Trust in this instance, they do not cite any diversity issue and agree that the policy is an acceptable professional requirement for everyone who works for the Trust in clinical areas."
Amid growing concern about the number of patients catching superbugs such as MRSA and Clostridium difficile while in hospital, the NHS introduced a new dress code for staff in January that was designed to prevent them transmitting bacteria.
The rules require all doctors and nurses who come into contact with patients to have their arms bare below the elbows, by wearing short-sleeved clothes or rolling up their sleeves. Jewellery, watches and false nails were also banned to reduce the risk of infection by staff.
However the policy was criticised by some Muslim doctors and medical students for going against the teachings of the Qu'ran on dress.
In the latest case, the radiographer was employed by an agency to work at the Royal Berkshire on June 16 this year and was told about the dress code.
The woman, who did not want to be identified, said she wants to "prevent the policy from being universally applied, so other Muslim women do not experience the same trauma."
Dr Majid Katme, spokesman for the Islamic Medical Association, said: "Any practising Muslim woman should have the right to cover her arms, as long as her job doesn't jeopardise the care of the patient.
"What's the harm in somebody in her position covering their arms, as people in radiography have done for some time?"