Kalina, 76, said the installation in the museum's fountain relates to John Paul II's efforts in the 1980s to help free Poland from communism, which is symbolized by the red color the water has from a red fabric placed on the fountain's bottom.
The sculpture also drew ridicule on social media, with some commenters comparing the life-sized likeness of the canonized pope toting a rock to a cartoon figure.
Cattelan's work, which was displayed in Warsaw in 2000, was seen as disrespectful and provoked a huge outcry.
Born as Karol Wojtyla in the southern Polish city of Wadowice, John Paul II served as pope from October 1978 until his death in April 2005.
Critics say that during his papacy, the church failed to bring priests who sexually abused children to account.