The woman's employer, Salmi & Partners, was outraged after the Supreme Migration Court ruled on Thursday to have the woman taken off the case.
"It's just pure discrimination. We're going to demand 100,000 kronor ($13,000) from the state for this violation," said Ismo Salmi at the firm.
Salmi & Partenrs has also vowed to request leave from the Supreme Administrative Court to appeal the verdict.
The lawyer at the centre of the row was appointed last autumn by the Migration Board to represent an Egyptian man seeking asylum in Sweden. The man, a Christian, said he and his family were seeking asylum on grounds of persecution by Muslims in their home country.
On realising that his legal counsel was to be a Muslim woman, the man asked to be assigned a different lawyer.
The Migration Board refused his request, arguing that the lawyer's religion did not constitute sufficient grounds for a switch. The man then turned to the Migration Court of Appeal, where he stated that he did not trust his lawyer, a veil-wearing Muslim woman, to best represent his interests.
The appeals court however reached the same conclusion as the Migration Board and declined to allow the asylum seeker the right to be assigned a new lawyer.
But the Egyptian man appealed again. This time, the Supreme Migration Court ruled in his favour, giving him the right to be assigned a lawyer who was not a Muslim.
Explaining its verdict, the court wrote that the man's grounds for seeking asylum were such that "his reaction to the situation is understandable."
At Salmi & Partners, Ismo Salmi said if the ruling were allowed to stand there was a serious risk that other law firms would think twice about employing lawyers who wore Muslim veils, as to do so might reduce their chances of getting work from the Migration Board.
"It's unbelievable that a superior court in Sweden can make a ruling like this. It's an incredible violation," he said.