Broadband imaging photometry, and broadband and narrowband linear polarimetry was measured for the nucleus of 2P/Encke over the phase-angle range 4 - 28 deg. An analysis of the point spread function of the comet reveals only weak coma activity, corresponding to a dust production of the order of 0.05 kg/s. The nucleus displays a color independent photometric phase function of almost linear slope. The absolute R filter magnitude at zero phase angle is 15.05 +/- 0.05, and corresponds to an equivalent radius for the nucleus of 2.43 +/- 0.06 km (for an adopted albedo of 0.047). The nucleus color V - R is 0.47 +/- 0.07, suggesting a spectral slope of 11 +/- 8 %/100nm. The phase function of linear polarimetry in the V and R filters shows a widely color independent linear increase with phase angle (0.12 +/- 0.02%/deg). We find discrepancies in the photometric and polarimetric parameters between 2P/Encke and other minor bodies in the solar system, which may indicate significant differences in the surface material properties and light-scattering behavior of the bodies. The linear polarimetric phase function of 2P/Encke presented here is the first ever measured for a cometary nucleus, and its analysis encourages future studies of cometary nuclei in order to characterize the light-scattering behavior of comets on firm empirical grounds and provide suitable input to a comprehensive modeling of the light scattering by cometary surfaces.