The local fields seen by positive muons implanted in Zn-doped La2CuO4 show a distribution with a main peak attributed to muon sites far from the Zn ions and a satellite structure corresponding to muons residing closer to the Zn. The temperature dependence indicates a strong loss of magnetic order for Cu moments near the Zn atoms. The data can be understood in terms of a model where a Zn ion not only introduces a vacancy in the magnetic Cu lattice but also creates a RKKY-type disturbance. The electron spin polarization around the Zn ions induces a change of the magnetic moments on surrounding Cu ions. The AF lattice is found to be strongly perturbed within a radius of 10 Angstrom around each Zn ion. Possible consequences for the superconductivity of the corresponding Sr-doped materials are discussed.