We study the interaction between a planar Fabry-Perot microcavity and a single embedded gold nanoparticle. We record spatially resolved white-light transmission spectra and show that the interaction between microcavity and nanoparticle gives rise to a redshift of the cavity modes, in accordance with the Bethe-Schwinger cavity perturbation formula. The spectral tuning of cavity modes by discrete nanoparticles can be exploited for applications such as optical and micromechanical sensing.