Noncontact Brillouin spectroscopy is a purely optical and label-free method to retrieve fundamental material viscoelastic properties. Recently, the extension to a three-dimensional imaging modality has paved the way to novel exciting opportunities in the biomedical field, yet the detection of the Brillouin spectrum remains challenging as a consequence of the dominant elastic background light that typically overwhelms the inelastic Brillouin peaks. In this Letter, we demonstrate a fully integrated and ultra-compact Brillouin notch filter based on an optical ring resonator fabricated on a silicon nitride platform. Our on-chip ring resonator filter was measured to have a 10 dB extinction ratio and a Q factor of 1.9x10^5. The experimental results provide a proof-of-concept on the ability of the on-chip filter to attenuate the elastic background light, heralding future developments of fully integrated, ultra-compact and low-cost Brillouin spectrometers.