Finite MoS2 nanoparticles are known to support metallic edge states that are responsible for their catalytic activity. In this work we employ time-dependent density-functional theory (TDDFT) to study the influence of such edge states on the optical properties of triangular MoS2 monolayer flakes. We find that the edge states support collective plasmon-like excitations that couple strongly to the optical field leading to pronounced absorption peaks below the onset of interband transitions on the basal plane. Additionally, structural relaxation of the flakes can significantly distort the edge states. Thus, we observe that while an evenly-spaced edge configuration supports one-dimensional (1D) plasmon modes similar to those of an ideal 1D electron gas, the relaxed structures show mixed plasmon and single-electron excitations in the low-energy response. Our findings illustrate the sensitivity of the optical response of MoS2 nanostructures to the details of the edge configuration.