The protests blocked many people from entering the theatre, the broadcaster said.
One person who got inside was taken away in an ambulance after allegedly being attacked with a corrosive, according to TVN reporter Tomasz Zieliński.
According to TVN, one of the protests made up of a few hundred people, some of them waving flags of a nationalist organisation, opposed the play which has been accused of inciting hatred and offending religious beliefs.
A counter-protest supported freedom of speech, TVN said.
Croatian director Oliver Frljić's play, called “The Curse” – an adaptation of Polish writer Stanisław Wyspiański's 1899 play of the same name – has been widely criticised since its premiere in Warsaw's Teatr Powszechny theatre in February.
Critics have slammed the play for scenes in which guns are made out of religious symbols and sex acts are performed on the leader of the Catholic church, who is also portrayed as about to be executed.
A top Polish official from the Catholic Church said the cross, a Christian symbol, is violated during performances, while insults directed at the late, Polish-born leader of the Church, Pope John Paul II, are "especially painful for Poles".
Following earlier protests against the play, Warsaw City Hall banned protests ahead of performances this month, but a court lifted that ban earlier this week, TVN said.
Frljić's “The Curse” explores the division of Church and state. It looks specifically at the influence of religion on people who declare themselves independent of the Church, but also on those who identify with Catholicism, Teatr Powszechny said.
It also tests the extent to which modern drama practices self-censorship in a bid to avoid “violating religious freedoms”, the theatre added.
The play is based on an 1899 drama about a drought in a small country town, which the local church leader said is God's vengeance for the sins of the villagers.
But the villagers blame the drought on the priest, who has two children and lives with their mother. Wyspiański's play was considered risqué when it was first performed. (vb)