The San Diego Union-Tribune says the council also approved a $2,000 study to determine how the piece can be removed without damage.
Encinitas is a well-known surfing spot.
Because it didn't have a public review process, the mosaic is legally considered graffiti. Council members say they personally like the piece but allowing it to remain on public property sets a bad precedent.
Some local businesses have offered to give the Madonna a home.