KOMOTINI, Greece—In this sliver of land on the border with Turkey, about 100,000 Greek citizens live with a relic of Greece’s historically fraught relations with its neighbor: Shariah law.

In Western Thrace, Shariah law is enforced for Muslim citizens, making Greece the world’s only non-Muslim country that officially applies laws grounded in the Islamic faith.

But that situation could soon be coming to an end, with the Greek government having submitted legislation this week that would make compliance with Shariah optional in the wake of a clash between Muslim rules and Greek laws. Government officials said it would become law before an international court rules that the current arrangement breaches Europe’s human-rights standards.

Meanwhile, Turkish President Recep Tayyip Erdogan is set on Friday to visit Thrace, where about a third of the 350,000 residents are Muslims who mostly speak Turkish. In a tense exchange with Greece’s president in Athens on Thursday, Mr. Erdogan said the rights of the region’s Turkish minority to uphold their traditions weren’t being properly honored.

His visit and his comments on the sensitive issue come on the heels of Wednesday’s debate in the European Court of Human Rights in Strasbourg, France, on whether to condemn Greece—where about 2% of the population is Muslim—for applying Shariah rules to family law.