Does an artist need to use public domain music when making a musical sculpture?

I guess it depends on whether you're being paid to produce the sculpture/whether patrons will have to pay to see it, etc.

If you are prepared to pay royalties for using the music you can use anything you want. If you want to use the music for free then, yes, you will have to limit yourself to what is in the public domain. The other issue beyong who holds the rights to the music is who is performing the music. If you are playing a recording of a public domain composition performed by the Boston Pops (for instance) then you may have to still pay the orchestra. The only way to get around that would be to find a musician (musicians) willing to perform the piece for you for whatever you are willing to pay or for free.