Victoria Wasteney, a senior occupational therapist, had worked for East London NHS Foundation Trust for eight years before she ran into trouble after being accused of "harassing and bullying" her co-worker by giving her a book about a Muslim woman's encounter with Christianity.
Earlier this year, the employment tribunal ruled that her employers were right to discipline Miss Wasteney for praying for her colleague, handing her a Christian book and inviting her to church events.
Her lawyers have now won the right to appeal the tribunal decision.
Judge Eady QC said the case raised points of law of public importance.
She said the Employment Appeal Tribunal should consider whether the original ruling had properly applied the European Convention on Human Rights' strong protection of freedom of religion and expression.
Miss Wasteney said: "I conducted all my conversations with my colleague in a sensitive and appropriate way. I knew she was from a different faith background and I was respectful of that. I didn't force my beliefs on anyone at any point. Surely there should be room for mutual conversations about faith, where appropriate, in the workplace?
"A complaint was made against me by someone who left the job the following month and who did not attend the NHS trust's disciplinary hearing or the Employment Tribunal. Evidence from text messages shows that we had a friendly relationship. I believe that the complaint has been handled in the way that it has because I am a Christian.
"I am relieved and pleased that the Employment Appeal Tribunal will now consider my case.
"There is already an unnatural caginess around faith and belief which is an obstruction to building meaningful relationships in the workplace and this case challenges that."
An appeal is expected to be heard next year.
Andrea Williams, chief executive of the Christian Legal Centre which is supporting Miss Wasteney, said: "We are delighted that permission to appeal has been granted and that the judge has recognised the importance of the issues at stake.
"Victoria's case raises crucial questions about how the European Convention on Human Rights' strong protection of religious freedom applies in the UK and about the extent to which employers can censor freedom of expression."