This paper presents an investigation on the spatial variation of the average field of a laser beam which is self‐focused in a plasma having random fluctuations in its electron concentration. The analysis is valid for the arbitrary mechanism of self‐focusing nonlinearity, for nonlinearly absorbing and nonuniform plasmas, and for elliptically Gaussian laser beams. The Novikov‐Furutsu formalism has been followed to derive a parabolic equation for the average field, and the Akhmanov approach has been employed to solve this equation. It is concluded that the plasma turbulence tends to reduce the field intensity as the laser beam penetrates further. The self‐focusing‐induced oscillations of the beamwidth parameters and axial intensity become considerably aperiodic in the presence of turbulence; after a sufficient distance of propagation, an oscillating beamwidth parameter (axial intensity) starts increasing (decreasing) monotonically.