A federal agency is suing Baystate Medical Center of Springfield for allegedly discriminating against an employee who refused to get the flu vaccine because of her Christian faith.

In the suit filed Thursday in US District Court in Springfield, the Equal Employment Opportunity Commission said Baystate unlawfully suspended and later fired the employee, Stephanie Clarke, because of her religion.

Baystate, like many hospitals, requires its workers to be vaccinated to prevent the spread of the flu virus. Those who refuse the vaccine must wear masks.

Clarke, who worked as a hiring consultant in the hospital’s human resources department, declined the flu shot because she lives according to the precepts of the Bible and “believes her body is a temple,’’ according to the lawsuit. Because of her religious beliefs, she rejects all injections, as well as drugs and vaccines, the ­complaint states.

Clarke wore a mask to comply with hospital policy, but the mask made it difficult for her to talk to job applicants, so she often pulled the mask away from her mouth when she was speaking.

The complaint alleges that Baystate suspended Clarke without pay in November for not wearing the mask properly at all times — even though she did not interact with patients. Clarke asked the hospital to come up with another accommodation that would not interfere with her job. But in December, the hospital terminated her employment and made her ineligible for rehire.

“Because Clarke’s job did not require her to have patient contact, it would not have been an undue hardship for [the hospital] to exempt Clarke from the flu vaccine requirement, or to permit her to remove the mask while speaking,’’ the complaint states.

Kevin Berry, New York district director for the Equal Employment Opportunity Commission, added in a statement, “Employees have the right to oppose conduct they reasonably believe violates the law, without fear of retaliation.’’

The agency said it filed suit after first trying to reach a settlement with Baystate. Its complaint demands that Baystate stop discriminating against employees and requests unspecified back pay and damages for Clarke, including ­compensation for “emotional pain, suffering, inconvenience, loss of ­enjoyment of life, humiliation, and loss of civil rights.’’

Baystate Medical Center is a teaching hospital owned by the nonprofit Baystate Health, the dominant health system in Western Massachusetts. Hospital spokesman Benjamin Craft declined to comment on pending litigation.

“Our patients’ safety is our highest priority, so we take all reasonable steps to minimize any risk of transmission of infectious illness such as flu,’’ Craft said in a statement. “That includes a requirement to be vaccinated against flu or wear a mask at all our facilities during flu season.’’

The Massachusetts Hospital ­Association has long advocated for mandatory flu vaccines, arguing that such policies boost vaccination rates. But such requirements have run into opposition, especially from the Massachusetts Nurses Association. The union filed a suit against Brigham and Women’s Hospital for its policy in 2014, but the suit was later dismissed. Nurses in the past have also protested vaccination policies at UMass Memorial Medical Center in Worcester.

The flu, or influenza, is a viral infection that sometimes causes complications and can be fatal. The Centers for Disease Control and Prevention recommend that almost everyone older than 6 months get a flu vaccine every year, but about half of all Americans skip their flu shots.

Priyanka Dayal McCluskey can be reached at priyanka.mccluskey@globe.com. Follow her on Twitter @priyanka_dayal.