Low-bandgap semiconductor nanowires (NWs) attract considerable interest for mid-infrared (MIR) photonics and optoelectronics, where ideal candidate materials require surface-passivated core–shell systems with large tunability in band offset, lineup, and emission wavelength while maintaining close lattice-matching conditions. Here, we propose and demonstrate epitaxial InAs–AlAsSb core–shell NW arrays on silicon (Si) that offer exceptional control over both the internal strain close to lattice-matching as well as band lineups tunable between type-I and type-II, with almost no analogue in the III–V materials family. We develop direct monolithic growth of high-uniformity InAs–AlAsSb NWs with wide tunability in shell composition and employ correlated Raman scattering and micro-photoluminescence spectroscopy to elaborate the interplay among hydrostatic strain, band lineup, and emission energy of the NW core luminescence tuned from ∼0.4 to 0.55 eV. Electronic structure calculations further support the experimentally observed tunability between type-I and type-II band lineups. The Si-integrated InAs-AlAsSb NW materials system holds large prospects not only for on-chip MIR photonics but also for other applications including high-speed transistors and NW-based hot carrier solar cells.