City authorities dispatched about 200 police to St Gergis church in the Muharram Bec neighbourhood in Alexandria on Friday to keep the demonstrators from entering and disrupting the play.
The production features a poor Christian university student who converts to Islam when a group of Muslim men promise him much-needed money.
When he becomes disenchanted with his decision, the men threaten him with physical violence to prevent him from returning to his original faith.
DVDs of the performance, entitled I Was Blind But Now I Can See, were being distributed by Coptic Christians, who make up about 10% of Egypt's population of 70 million.
Abdel Moneim Mahmoud, a Muslim in Alexandria, said that he had watched a recording of the play and found it "offending".
The protesters have given the church a week to apologise and dismiss its priest, Aljazeera's correspondent in Egypt said.
"It tells you how Muslims are all terrorist and how they deceive Christians to convert to Islam either by force or money," Mahmoud said.
Church officials could not be reached for comment.
Accusations of forced conversions are routine in Egypt.
In December, angry Copts protested in Cairo for four days and clashed with police when the wife of a priest fled her home in the south to convert to Islam.
She later returned home and resumed practising Christianity.