Dirac and Weyl semimetals, such as cadmium arsenide (Cd3As2), have recently attracted attention for use in high-speed photodetectors that operate at longer infrared wavelengths, where conventional semiconductor-based photodetectors have a limited performance. In this Letter, we explore near-infrared (960 nm) photodetection in a Cd3As2/AlSb heterojunction. We show that Cd3As2/AlSb heterojunctions allow for an unbiased operation and demonstrate an enhanced responsivity and quantum efficiency compared to AlSb and Cd3As2 reference devices. To characterize their high-speed response, the photocurrent dynamics of the heterojunctions were also explored via time-resolved photocurrent (TRPC) measurements, revealing a photocurrent process occurring over 200-500 ps in the Cd3As2/AlSb heterojunctions that is not observed in the AlSb and Cd3As2 reference devices. This time is attributed to the recombination rate of carriers in the heterojunction.