Case offier Hanna Wilson says the ruling is a landmark decision for the anti-discrimination watchdog.
"This is the first time we have decided that a language policy may be indirect discrimination," she said.
A similar complaint against a school kitchen ruled that its Swedish-only policy was not discriminatory because it was "a recommendation and not a prohibition."
Folktandvården Stockholm, which owns and runs 52 clinics in and around the Swedish capital, insists that its employees, nearly half of whom were born outside Sweden, only speak Swedish in the workplace. The only exception is when a patient does not speak Swedish.
In its ruling, the ombudsman accepted that the policy was designed to make it easier for staff to socialise and work together, but said that it was nonetheless discriminatory.
"The policy may in fact put people of a certain ethnicity at a particular disadvantage because the policy meant that employees with another mother tongue than Swedish didn't have the same possibility to speak their mother tongue," Wilson explains.
A Persian-speaking dentist last year appealed to the ombudsman after the head of the clinic where she worked reprimanded her for not speaking Swedish.
The ombudsman published its ruling on October 10.
Åsa Brandt, a spokesperson for Folktandvården Stockholm, said that because the ruling was not binding, there were no immediate plans to change the policy.
"We are not going to chage the policy right now at the moment, but we will of course take on board the ombudsman's ruling," she said.