Christian charity ADF International is supporting Ellinor Grimmark's case.
Her lawyers are arguing that under EU law, she should not be required to carry out abortions because healthcare professionals are entitled to "freedom of conscience" over pregnancy termination.
The lawyers also argue that performing abortions is a "very limited part of the work" of Swedish midwives and she can perform the other duties the job requires.
ADF's Director of European Advocacy, Robert Clarke, says "nobody should be forced to choose between following their conscience and pursuing their profession".
But Mia Ahlberg, president of the Swedish Association of Midwives told the BBC that Grimmark should choose another profession if she is unwilling to perform abortions.
Ahlberg added that if Grimmark wins the case, it would have consequences for the whole Swedish health care system.
She said: "For example, a nurse who is a Jehovah's Witness might refuse to perform a blood transfusion.
"It's part of our professional competence - so the employer had a right to say 'you cannot work here'."
Her case was initially rejected at a local level in 2015 and the court ordered that she should pay the legal costs of the health authority.
Sweden has one of the highest abortion rates in Europe with 20.8 abortions being performed out of 1000 women in 2011 according to the UN.