We study the impact of dynamical correlations on the electronic structure and coherent transport properties of Cu nanocontacts hosting a single magnetic impurity (Ni,Co,Fe) in the contact region. The strong dynamical correlations of the impurity 3d-electrons are fully taken into account by combining density functional calculations with a dynamical treatment of the impurity 3d-shell in the one-crossing approximation. We find that dynamical correlations give rise to the Kondo effect and lead to Fano features in the coherent transport characteristics similar to those observed in related experiments. ; Comment: accepted for publication in Phys. Rev. Lett.; replaced with accepted version of manuscript; 5 pages, 3 figures