A strong reduction of the spatial coherence of a laser beam after its propagation through a plasma has been measured using a Fresnel biprism interferometer. The laser beam was diffraction limited; the coherence width was reduced from 40 mm in vacuum down to a few mm with the plasma. Numerical results based on a paraxial model exhibit a coherence degree close to the experimental one; they also prove the importance of taking into account the nonlocal transport effects in numerical simulations for such plasma conditions.