Najat Abokal, a lawyer representing the woman, said the order was made for divorce proceedings in the district court in Luckenwalde, Brandenberg.
She said the letter warned of legal action against the woman if she does not comply, but also ordered her to appear in person to present her case against her husband.
One of her colleagues confirmed the information to The Independent but said no further comment could be given while the case continued.
A spokesperson for the district court in Luckenwalde said they could not comment, saying the judge was responsible for conduct within the courtroom.
The German parliament has voted in favour of a partial ban on the burqa and other Islamic veils that cover the face, while existing “neutrality” laws can be used to forbid the wearing of any religious or political symbols by some judicial officials.
But the restrictions do not apply to witnesses, claimants, victims or any other participants in legal proceedings, while a 2006 ruling by the Federal Constitutional Court found a judge had no right to throw out a spectator for wearing a headscarf..
Klaus F Gärditz, an law professor at Bonn’s Friedrich-Wilhelms University, described the letter as an attempt to “humiliate” the woman that violates freedom of religion.
He accused the judge of “pursuing provincial racism and sexism under the pretext of following legal procedures”, noting that only women were affected by such orders in an article for the Legal Tribune Online.
The case comes amid intense debate over Islamic veils in Germany, where a law to partially ban the burqa – but not the hijab (headscarf) – has not yet come into force.
Angela Merkel announced her support for the move in December, saying full-face veils were “not acceptable in Germany” and calling them to be banned “wherever it is legally possible”.
Some right-wing politicians have called for a full ban on the burqa in public, which has been imposed in France and Belgium, but ministers have said a blanked prohibition would violate the country’s constitution.
A poll carried last year showed that 81 per cent of Germans supported a ban on the burqa within public institutions.
Dutch MPs voted for a similar prohibition in the Netherlands last year, covering public transport, education, healthcare and government buildings and punishing any infractions with fines.
Attempts to ban female employees from wearing headscarves and veils have sparked several legal cases, which have so far seen the European Court of Human Rights and European Court of Justice support national prohibitions.
In the UK, an estate agent is suing her former employer at a tribunal after she was allegedly told to remove her black hijab because it had “terrorist affiliations”.