Farah Alhajeh, 24, was applying for a job as an interpreter when she declined to shake the hand of a male interviewer for religious reasons.
She placed her hand over her heart in greeting instead.
Alhajeh had been hoping to land a job as an interpreter with the company after the May 2016 interview. Instead, she said she was escorted to the elevator, the interview abruptly over.
"As soon as I got to the elevator, I cried," she told Swedish news channel SVT. "It had never happened to me before."
The Swedish labour court ruled the company had discriminated against her and ordered it to pay 40,000 kronor ($4,350; £3,420) in compensation.
Sweden's labour court found the company was justified in demanding equal treatment for both sexes - but not in demanding that it be in the form of a handshake only.
Her refusal to shake hands on religious grounds was protected by the European Convention on Human Rights, it said, and the company's policy in demanding a specific greeting was detrimental to Muslims.
The court also disagreed with the firm's assertion that Ms Alhajeh's approach to greetings would cause a problem for effective communication as an interpreter.
However the judges were divided over the case - with three supporting Ms Alhajeh's claim and two voting against.
Alhajeh told the BBC she respects Sweden's gender equality and thus does not shake anybody's hand.
"I don't have any physical contact with men or with women," she said. "I can live by the rules of my religion and also at the same time follow the rules of the country that I live in."