Kerr beam cleaning is a nonlinear phenomenon in graded-index multimode fiber where power flows toward the fundamental mode, generating bell-shaped output beams. Here we study beam cleaning of femtosecond pulses accompanied by gain in a multimode fiber amplifier. Mode-resolved energy measurements and numerical simulations showed that the amplifier generates beams with high fundamental mode content (greater than 30% of the overall pulse energy) for a wide range of amplification levels. Control experiments using stretched pulses that evolve without strong Kerr nonlinear effects showed a degrading beam profile, in contrast to nonlinear beam cleaning. Temporal measurements showed that seed pulse parameters have a strong effect on the amplified pulse quality. These results may influence the design of future high-performance fiber lasers and amplifiers.