Altermagnet is an emerging antiferromagnetic material subclass that exhibits spin-splitting in momentum space without net global magnetization and spin-orbit-coupling effect. In this work, we develop a model of thermal charge injection across an altermagnet/semiconductor (AM/S) Schottky contact. We obtain analytical expressions describing the spin-dependent thermionic current injection across the AM/S contact under any arbitrary interface orientation angles. Interestingly, the spin-contrasting Fermi surface of an altermagnetic electrode enables spin-polarized current to be injected into a nonmagnetic semiconductor even though the system has net-zero magnetization. Our findings thus reveal an altermagntic mechanism to achieve spin injection without involving ferromagnetic ordering. The AM/S Schottky contact proposed here shall provide a potential altermagnetic building block of spintronic devices that are resilient against stray magnetic field perturbation and inherently compatible with ultracompact integration.