The control of optical and transport properties of semiconductor heterostructures is crucial for engineering new nanoscale photonic and electrical devices with diverse functions. Core–shell nanowires are evident examples of how tailoring the structure, i.e., the shell layer, plays a key role in the device performance. However, III–V semiconductors bandgap tuning has not yet been fully explored in nanowires. Here, a novel InAs/AlSb core–shell nanowire heterostructure is reported grown by molecular beam epitaxy and its application for room temperature infrared photodetection. The core–shell nanowires are dislocation‐free with small chemical intermixing at the interfaces. They also exhibit remarkable radiative emission efficiency, which is attributed to efficient surface passivation and quantum confinement induced by the shell. A high‐performance core–shell nanowire phototransistor is also demonstrated with negative photoresponse. In comparison with simple InAs nanowire phototransistor, the core–shell nanowire phototransistor has a dark current two orders of magnitude smaller and a sixfold improvement in photocurrent signal‐to‐noise ratio. The main factors for the improved photodetector performance are the surface passivation, the oxide in the AlSb shell and the type‐II bandgap alignment. The study demonstrates the potential of type‐II core–shell nanowires for the next generation of photodetectors on silicon.