Let $k$ be a field of characteristic zero and $f$ be a non constant function defined on a smooth variety. We construct in this article a motivic Milnor fiber at infinity which belongs to a Grothendieck ring of varieties. It is defined in terms of a chosen compactification, not necessary smooth, but is shown to be independent of this choice. When $k$ is the field of complex numbers, using the Hodge realization morphism, it specializes to the spectrum at infinity of $f$. As an example, we compute it in the case of a Laurent polynomial non-degenerated with respect to its Newton polyhedron at infinity. For each value $a$, we define a complete motivic Milnor fiber $S_{f,a}$. This object is an extension of the usual motivic Milnor fiber $S_{f-a}$. Then we introduce motivic atypical values, a motivic bifurcation set of $f$ and a notion of motivically tame function.