The mechanical exfoliation of naturally occurring layered materials has emerged as an easy and effective method for achieving ultrathin van der Waals (vdW) heterostructures with well-defined lattice orientations of the constituent two-dimensional (2D) material layers. Cylindrite is one such naturally occurring vdW heterostructure, where the superlattice is composed of alternating stacks of SnS2-like and PbS-like layers. Although the constituent 2D lattices are isotropic, inhomogeneous strain occurring from local atomic alignment for forcing the commensuration makes the cylindrite superlattice structurally anisotropic. Here, we demonstrate the highly anisotropic optical responses of cylindrite thin flakes induced by the anisotropic crystal structure, including angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent anisotropic third-harmonic generation. Our results provide a promising approach for identifying various natural vdW heterostructure-based 2D materials with tailored optical properties and can be harnessed for realizing anisotropic optical devices for on-chip photonic circuits and optical information processing.