We discuss static spherically symmetric solutions in a recently proposed nonlocal infrared modification of Einstein equations induced by a term m 2 g μν □−1 R, where m is a mass scale. We find that, contrary to what happens in usual theories of massive gravity, in this nonlocal theory there is no vDVZ discontinuity and classical non-linearities do not become large below a Vainshtein radius parametrically larger than the Schwarzschild radius r S . Rather on the contrary, in the regime r ≪ m −1 the corrections to the metric generated by a static body in GR are of the form 1 + O (m 2 r 2) and become smaller and smaller toward smaller values of r. The modification to the GR solutions only show up at r ≳ m −1. For m = O (H 0), as required for having interesting cosmological consequences, the nonlocal theory therefore recovers all successes of GR at the solar system and lab scales