Is electronvolt a mass or an energy unit?

Strictly speaking it's a unit of energy. But using $m=\frac{E}{c^2}$, you can convert energy into mass. Operating, we get $1{\rm\,eV}/c^2 =1.78\cdot 10^{-36}\rm{\,kg}$. (The $c^2$ is usually ommited.)

It is absolutely a unit of energy, though your confusion may arise due to the usage of what's known as geometrized units, where c the speed of light (in addition to the gravitational constant G) is set to unity. This is typically done in General Relativity. In this system, mass and energy have exactly the same units - they are two sides of the same coin.