Aims. We predict the exoplanet yield of a space-based mid-infrared nulling interferometer using Monte Carlo simulations. We quantify the number and properties of detectable exoplanets and identify those target stars that have the highest or most complete detection rate. We investigate how changes in the underlying technical assumptions and uncertainties in the underlying planet population impact the scientific return. Methods. We simulated 2000 exoplanetary systems, based on planet occurrence statistics from Kepler with randomly orientated orbits and uniformly distributed albedos around each of 326 nearby (d< 20 pc) stars. Assuming thermal equilibrium and blackbody emission, together with the limiting spatial resolution and sensitivity of our simulated instrument in the three specific bands 5.6, 10.0, and 15.0 μm, we quantified the number of detectable exoplanets as a function of their radii and equilibrium temperatures. Results. Approximately 315-77+113 exoplanets, with radii 0.5 REarth ≤ Rp ≤ 6 REarth, were detected in at least one band and half were detected in all three bands during ~0.52 years of mission time assuming throughputs 3.5 times worse than those for the James Webb Space Telescope and ~40% overheads. Accounting for stellar leakage and (unknown) exozodiacal light, the discovery phase of the mission very likely requires 2−3 years in total. The uncertainties in planet yield are dominated by uncertainties in the underlying planet population, but the distribution of the Bond albedos also has a significant impact. Roughly 50% of the detected planets orbit M stars, which also have the highest planet yield per star; the other 50% orbit FGK stars, which show a higher completeness in the detectability. Roughly 85 planets could be habitable (0.5 REarth ≤ Rp ≤ 1.75 REarth and 200 K ≤ Teq ≤ 450 K) and are prime targets for spectroscopic observations in a second mission phase. Comparing these results to those of a large optical/near-infrared telescope, we find that a mid-infrared interferometer would detect more planets and the number of planets depends less strongly on the wavelength. Conclusions. An optimized space-based nulling interferometer operating in the mid-infrared would deliver an unprecedented dataset for the characterization of (small) nearby exoplanets including dozens of potentially habitable worlds.