Police made the arrests at the Theatre de la Ville, on the banks of the Seine near Notre Dame cathedral, during a performance of "On the Concept of the Face, Regarding the Son of God", directed by Italian Romeo Castellucci.
The play, which runs until October 30th, is the story of an incontinent man being looked after by his son.
A copy of a huge portrait of Christ by Renaissance artist Antonello da Messina hangs at the back of the stage and appears to be covered in excrement towards the end of the performance.
After days of trying to get in, the protesters on Wednesday "entered the theatre and threw stink bombs into the auditorium, shouting: 'Enough Christianophobia!'" a police source told AFP.
France's ministry of culture blamed the demonstration on members of the Institut Civitas, which in April protested US artist Andres Serrano's renowned "Immersion Piss Christ" photograph in the southern papal city of Avignon.
Civitas head Alain Escada said: "Our mission is to spread the word about this performance and to organise a response."
A spectator described the protesters as "very young people who are very angry but very well dressed." Faced with a police cordon, they threw eggs and oil at the theatre and those going in, chanting in Latin or praying on their knees.
The association of French Roman Catholic bishops on Tuesday condemned "the violence perpetrated during recent performances... France's Roman Catholic Church is neither fundamentalist nor obscurantist (opposed to enlightenment)."
Dramatic luminaries including Juliette Binoche and Michel Piccoli have joined a committee to support the theatre, while Civitas has called for a mass demonstration "in Christ's honour".
"It's insulting at the end of a scatological play to sully the portrait of Christ by making people believe that it's faecal matter that has dirtied it, wounding so many believers," the Insitut Civitas said on its website.