We demonstrate the existence of the spectral phase shift a pulse experiences when it is subjected to spectral focusing. This π/2 phase shift is the spectral analog of the Gouy phase shift a 2D beam experiences when it crosses its focal plane. This spectral Gouy phase shift is measured using spectral interference between a reference pulse and a negatively chirped parabolic pulse experiencing spectral focusing in a nonlinear photonic crystal fiber. To avoid inherent phase instability in the measurement, both reference and parabolic pulses are generated with a 4-f pulse shaper and copropagate in the same fiber. We measure a spectral phase shift of π/2, reaffirming its generality as a consequence of wave confinement in the spatial, temporal and spectral domains.