The statue, "The Virgin Mother" by British artist Damien Hirst, sits on a conservation easement of the historic Old Westbury estate of real estate mogul Aby Rosen.
Officials say the village has strict rules regulating easements, and the statue was installed without proper permitting and architectural board approval. The statue previously sat in the courtyard at Lever House in midtown.
The village is considering limiting such "accessory structures" to a height of 25 feet. A hearing on the issue is set for May 19.
According to his website, Hirst has created several versions of the piece, which he says is posed in a way to recall Edgar Degas' "Little Dancer of Fourteen Years."
Hirst said the reference to Degas "is kind of naughty; she shouldn't really be pregnant. I wanted a feeling of that."
Rosen had no comment, according to Newsday.