This paper presents a deep MIRI/JWST medium-resolution spectroscopy (MRS) covering the rest-frame optical spectrum of the GN-z11 galaxy. The [O III] 5008 Å and Hα emission lines are detected and spectroscopically resolved. The line profiles are well modeled by a narrow Gaussian component with intrinsic full widths at half maximum of 189 ± 25 and 231 ± 52 km s-1, respectively. We do not find any evidence of a dominant broad Hα emission line component tracing a broad-line region in a type 1 active galactic nucleus (AGN). The existence of an accreting black hole dominating the optical continuum and emission lines of GN-z11 is not compatible with the measured Hα and [O III] 5008 Å luminosities. If the well-established relations for low-z AGNs apply in GN-z11, the [O III] 5008 Å and Hα luminosities would imply extremely high super-Eddington ratios (λE > 290), and bolometric luminosities ∼20 times those derived from the UV/optical continuum. However, a broad (∼430-470 km s-1) and weak (< 20-30%) Hα line component, tracing a minor AGN contribution in the optical, cannot be completely ruled out with the sensitivity of the current data. The physical and excitation properties of the ionized gas are consistent with a low-metallicity starburst with a star formation rate of 24 ± 3 M⊙ yr-1. The electron temperature of the ionized gas is Te (O++) = 14 000 ± 2100 K, while the direct-Te gas-phase metallicity is 12 + log(O/H) = 7.91 ± 0.07 (Z = 0.17 ± 0.03 Z⊙). The optical line ratios locate GN-z11 in the starburst or AGN region, but they are more consistent with those of local low-metallicity starbursts and high-z luminous galaxies detected at redshifts similar to GN-z11. We conclude that the MRS optical spectrum of GN-z11 is consistent with that of a massive, compact, and low-metallicity starburst galaxy. Its high star formation and stellar mass surface densities are close to those of the densest stellar clusters, and we therefore speculate that GN-z11 might undergo a feedback-free, highly efficient starburst phase. Additional JWST data are needed to validate this scenario and other recently proposed alternatives to explain the existence of bright compact galaxies in the early Universe.