Understanding the impact of lateral mode confinement in plasmonic waveguides is of fundamental interest regarding potential applications in plasmonic devices. The knowledge of the frequency-wave vector dispersion relation provides the full information on electromagnetic field propagation in a waveguide. This Letter reports on the measurement of the real part of the surface plasmon polariton dispersion relation in the near infrared spectral regime for individual nanoscale plasmonic waveguides, which were formed by deposition of para-hexaphenylene (p-6P) based nanofibers on top of a gold film. A detailed structural characterization of the nanofibers provides accurate information on the dimensions of the investigated waveguides and enables us to quantify the effect of mode confinement by comparison with experimental results from continuous p-6P films and calculations based on the effective index method.