Time-resolved all-optical techniques are used to measure the density and temperature dependence of electron-hole recombination in an InAs/GaInSb/InAs/AlGaInAsSb strain-balanced superlattice grown by molecular beam expitaxy on GaSb. This 4 μm bandgap structure, which has been designed for suppressed Auger recombination, is a candidate material for the active region of mid-infrared lasers. While carrier lifetime measurements at room temperature show unambiguous evidence of Auger recombination, the extracted Auger recombination rates are considerably lower than those reported for bulk materials of comparable bandgap energy. We find that the Auger rate saturates at carrier densities comparable to those required for degeneracy of the valence band, illustrating the impact of Fermi statistics on the Auger process. The measured results are compared with theoretical Auger rates computed using a band structure obtained from a semi-empirical 8-band K.p model. We find excellent agreement between theoretical and experimental results when Umklapp processes in the growth direction are included in the calculation. Measured recombination rates from 50 to 300 K are combined with calculated threshold carrier densities to determine a material To value for the superlattice.