Anisotropic mechanical properties are a feature of many load-bearing tissues, such as muscles or blood vessel walls, which typically contain preferentially oriented collagen or elastin fibers embedded in a hydrated matrix. Measuring the anisotropy on a microstructural scale is important for modeling tissues' mechanical response, but has been difficult to obtain noninvasively. Here, we employ Brillouin microscopy to characterize the anisotropy of corneal tissues. We use angle-resolved Brillouin measurements to determine the longitudinal moduli of the ex vivo porcine cornea, assuming a lamellar, transverse isotropic model. We also observe significant anisotropy in Brillouin maps of the human cornea in vivo.