Semiconductor devices have become indispensable for generating electromagnetic radiation in everyday applications. Visible and infrared diode lasers are at the core of information technology, and at the other end of the spectrum, microwave and radio-frequency emitters enable wireless communications. But the terahertz region (1-10 THz; 1 THz = 10(12) Hz) between these ranges has remained largely underdeveloped, despite the identification of various possible applications--for example, chemical detection, astronomy and medical imaging. Progress in this area has been hampered by the lack of compact, low-consumption, solid-state terahertz sources. Here we report a monolithic terahertz injection laser that is based on interminiband transitions in the conduction band of a semiconductor (GaAs/AlGaAs) heterostructure. The prototype demonstrated emits a single mode at 4.4 THz, and already shows high output powers of more than 2 mW with low threshold current densities of about a few hundred A cm(-2) up to 50 K. These results are very promising for extending the present laser concept to continuous-wave and high-temperature operation, which would lead to implementation in practical photonic systems.