Sister Cristina Scuccia has since signed for record company Universal, which is releasing her album in November.
The original song courted controversy for its music video, which showed Madonna kissing a black Jesus.
Sister Cristina told The Guardian: "I chose it myself. Without any desire to provoke or scandalise.
"If you read the lyrics without being influenced by what has gone before, you discover that it is a song about the capacity of love to make people new again. To release them from their past. And this is how I wanted to interpret it."
She added that her rendition of the song was more "a secular prayer than a pop song".
Some of the lyrics have been changed or removed completely in Sister Cristina's cover.