Brillouin imaging of turbid biological tissues requires an effective rejection of the background noise due to elastic scattering of probe laser light. We have developed a narrowband spectral notch filter based on a pair of a free-space Fabry-Perot etalon and a mirror. The etalon filter in a 4-pass configuration is able to suppress elastically-scattered laser light with a high extinction ratio of > 40 dB and transmit inelastically-scattered light in a frequency shift range of 2-14 GHz with only 2 dB insertion loss. We also describe a simple etalon that enables us to use semiconductor diode laser sources for Brillouin microscopy by removing spontaneous emission noise. Using a clinically-viable Brillouin microscope employing these filters, we demonstrate the first Brillouin confocal imaging of the sclera and conjunctiva of the porcine eye.