The woman had been called to a job interview in Uppsala with a company providing interpretation services via telephone or video. But when the handshaking disagreement emerged, the company called off the ongoing interview, according to a statement by DO.
"In the first place, DO questions that the company at the time had a neutrality policy aimed at religious expressions, but believes in any case that such a policy had not been applied in a consistent and proportionate way," reads the statement, issued on Monday.
Last month the European Court of Justice ruled that employers are entitled in certain circumstances to require employees to for example dress neutrally in line with the company's image, meaning that a ban on the "visible wearing of any political, philosophical or religious sign in the workplace" could be legal.
"However, a prerequisite is that those limitations are demonstrated in existing policy and applied consistently and in a non-discriminatory manner," said DO, adding that because the woman would not be required to meet her customers in person, such a ban could not be enforced in this particular case.
"The ruling also shows that the interest in neutrality cannot be used to restrict religious expression for employees who do not have visual contact with customers," it added.
"Because this concerned a non-visible act which would not be expressed in telephone or video interpretation, it seems difficult to assert that it is something that would affect the brand," said Martin Mörk, head of DO's unit for processing cases.
DO is now taking the case to the Swedish Labour Court, demanding that the Uppsala company pay out 80,000 kronor (approximately $9,000) in damages to the woman.
There have been a number of similar rows over handshaking in Sweden in the past year. In July, a man sued a local council after he lost his job for refusing to shake hands with female colleagues. Lund District Court began looking at the case late last mont and is expected to announce its verdict in early April.
The most high-profile case meanwhile was that of a former Green Party politician who resigned a year ago due to controversy caused by his refusal to shake a TV reporter's hand in an interview.
Similar debates have also been raging in other countries. In Switzerland, two teenage boys raised the hackles of some politicians when it emerged that they had refused to shake the hands of female teachers.