No, it's not a fossilized musical instrument (though a carved animal bone thought be some to be a Neaderthal flute was found in 1995 in Slovenia). This is a xylophone made from fossils, in this case fossilized corals called Hexagonaria (Paleobiology Database, Wikipedia). Artist Tom Kaufmann carved an instrument from this stone, and plays (appropriately enough) the "Flintstones" theme song on it in this video:
He has made other instruments out of stone, which he calls "lithophones". Read more about his work on the Mental Floss blog.
These fossil corals are known as Petoskey Stone in the state of Michigan in the USA, where they are the official "state stone". The corals get their name from the six-sided appearance of the walls separating the individual corallites, which can be seen in the close-up at the beginning of the video, as well as in this brochure (pdf) from the Michigan state government.
As far as musical instruments made from living (or formerly living) organisms go, it's at least not as terrifying as the possibly apocryphal "cat piano".