We demonstrate tuning of infrared Mie resonances by varying the carrier concentration in doped semiconductor antennas. We fabricate spherical silicon and germanium particles of varying sizes and doping concentrations. Single-particle infrared spectra reveal electric and magnetic dipole, quadrupole, and hexapole resonances. We subsequently demonstrate doping-dependent frequency shifts that follow simple Drude models, culminating in the emergence of plasmonic resonances at high doping levels and long wavelengths. These findings demonstrate the potential for actively tuning infrared Mie resonances by optically or electrically modulating charge carrier densities, thus providing an excellent platform for tunable metamaterials.