Destruction of the Kondo effect by a local measurement

We show that the local spin measurement which decoheres the localized spin in a Kondo system, suppresses the Abrikosov-Suhl resonance and destroys the Kondo effect. This happens due to elimination of the entanglement between the localized spin and the conduction electrons, and differs essentially from smearing of the resonance by dissipation. Considering decoherence by a spin bath, we predict that the Kondo effect disappears when the Kondo temperature becomes smaller than the coupling with a bath. This effect can be detected in experiments on ``quantum corrals'' or quantum dots doped by impurities with internal degrees of freedom.