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Quantum spin liquids (QSLs) are exotic states of matter with fractionalized excitations and topological order. Kitaev QSL is distinct from other QSLs as the fractionalized excitations are Majorana fermions, yielding non-abelian anyons critical for topological quantum computations. It is thus highly desirable to detect a sign of the fractionalized particles in a spatially resolved manner toward locally controlling them. Here, using spectroscopic-imaging scanning tunneling microscopy, we report anomalous spatial oscillations of the local density of states around defects of monolayer α-RuCl₃, one of the most promising Kitaev QSL candidates. The oscillation decays away from the defects, is incommensurate, and exhibits a characteristic bias dependence. It therefore is distinguished from known oscillatory phenomena, such as charge density waves, Friedel oscillations, and quasiparticle interference. The oscillation characteristics indicate the presence of itinerant fermionic quasiparticles, implying that the oscillation manifests an unexpected feature of Kitaev QSL.