Hana Khatib, an attorney from the northern town of Tamra, became a qadi, judge in arabic, in the Muslim court system that deals with personal law at a ceremony in the presidential residence in Jerusalem.
"This appointment and my success in achieving it is a success for the legal system and for women," she told AFP after the ceremony.
"We see that the sharia system is kind to women and with this achievement we give them their rights."
Israeli President Reuven Rivlin, who hosted the swearing-in ceremony, said he hoped the appointment would be a first step and that other courts, including Jewish ones, would follow suit.
"This is testament to the positive changes in the status of women," he said.
"I allow myself to express the hope that the appointment of the first female religious judge will be the first of many, not just in the Muslim community."
Justice Ministry Ayelet Shaked was also in attendance, as were a number of Arab Israeli parliamentarians and senior figures.
President of the Islamic Sharia Court Sheikh Abdel al- Hakim Samara also hailed the appointment, saying it would be the "first in a series" of women serving in religious courts.
In Israel, family law -- divorce, marriage, endowments -- falls under the jurisdiction of religious courts, and separate systems exist for the country's different creeds.
There are not many women qadis around the world. Two women serve as sharia judges in the neighbouring Palestinian Authority.
Making up around 18 percent of Israel's population, Arab Israelis are descended from Palestinians who remained on their land after Israel was established.