According to the unpublished Superman story The K-Metal from Krypton, yes it is metal.
The DC Wiki also claim's it's a metal.
Green Kryptonite is the most common form of Kryptonite. It exists primarily as a metallic ore, but can also be found in crystalline forms.
However, in the official DC canon, it probably isn't.

Here are some properties of metals:
- Luster (shininess)
- Good conductors of heat and electricity
- High density (heavy for their size)
- High melting point
- Ductile (most metals can be drawn out into thin wires)
- Malleable (most metals can be hammered into thin sheets)
- Corrode easily. Corrosion is a gradual wearing away. (Example: silver tarnishing and iron rusting)
As you can see Kryptonite isn't shiny, doesn't conduct electricity, isn't ductile or malleable and it doesn't corrode easily.
So it probably isn't a metal.
So Kryptonite is all these things.
– Mar 28 '16 at 22:58