We report the observation of the generation and routing of single plasmons generated by localized excitons in a WSe$_2$ monolayer flake exfoliated onto lithographically defined Au-plasmonic waveguides. Statistical analysis of the position of different quantum emitters shows that they are $(3.3 pm 0.7)times$ more likely to form close to the edges of the plasmonic waveguides. By characterizing individual emitters we confirm their single-photon character via the observation of antibunching of the signal ($g^{(2)}(0) = 0.42$) and demonstrate that specific emitters couple to the modes of the proximal plasmonic waveguide. Time-resolved measurements performed on emitters close to, and far away from the plasmonic nanostructures indicate that Purcell factors up to $15 pm 3$ occur, depending on the precise location of the quantum emitter relative to the tightly confined plasmonic mode. Measurement of the point spread function of five quantum emitters relative to the waveguide with <50nm precision are compared with numerical simulations to demonstrate potential for higher increases of the coupling efficiency for ideally positioned emitters. The integration of such strain-induced quantum emitters with deterministic plasmonic routing is a step toward deep-subwavelength on-chip single quantum light sources.