We demonstrate a simple and robust single-shot interferometric technique that allows the in situ measurement of intensity-dependent phase changes experienced by ultrashort laser pulses upon nonlinear propagation. The technique is applied to the characterization of carrier-envelope phase noise in hollow fiber compressors both in the pressure gradient and in the static cell configuration. Measurements performed simultaneously with conventional f-to-2f interferometers before and after compression indicate that the noise emerging in the waveguide adds up arithmetically to the phase noise of the amplifier, thus being strongly correlated to the phase noise of the pulses coupled into the compressor.