The woman's lawyers are now considering whether to seek a judicial review.
The Muslim Council called for calm and said it recognised that the judge had attempted to balance the woman's religious rights with the needs of the court.
Talat Ahmed, chair of the council's social and family affairs committee, said: "Every time we discuss the niqab, it usually comes with a diet of bigoted commentary about our faith and the place of Islam in Britain. There are few people who wear the niqab, and they should be allowed to wear this veil if they freely decide to do so."
She said banning the garment was "un-British" and would mean "embarking on a slippery slope where the freedom to wear religious attire of all faiths would be at risk".
In his 35-page ruling Murphy, sitting at Blackfriars Crown Court, said he had sought to take the "least restrictive approach" to the issue.
The woman denies attempting to intimidate a witness. When she stands trial in November the court will be adjourned and cleared to allow her to identify herself to a female court officer. When she gives evidence with her face uncovered she will be able to do so from behind a screen or via video-link so she will not be on view.
The judge also took the unusual step of banning court drawings - a move likely to be challenged by media groups.
If she refuses to remove the veil she will not be able to testify.
- Independent