There are general mommy and me music classes, sure. But not formal lessons, which is what the op appears to be looking for. A toddler is not capable of taking formal music lessons. Fun classes to introduce music and songs and let them bang around on a variety of instruments are much more appropriate.
Yes, formal lessons. I was in private, formal music lessons, playing an actual (not toy) instrument, from a little under 2 1/2. As were many other kids in the school. It's not rare, there are methods besides Suzuki's, though he popularized it, but it exists many places.
As I said the school I attended is still in business and I believe starts at 2, for a variety of instruments.