Edit: I no longer agree with my answer, and I think it would be appropriate to accept one of the other answers. Depending on what you mean by the spacetime interval, it's either a non-local, non-tensorial thing (if we're talking about $\Delta s$), or a 2-form that happens to be preserved by Lorentz transformations (if we're talking about $ds^2$).
The spacetime interval is Lorentz invariant. That is, it is a scalar. A scalar is a particular case of a tensor. One could call it a (0,0)-tensor (as in zero covariant and zero contravariant indices).