Silicon, germanium, and related alloys, which provide the leading materials platform of electronics, are extremely inefficient light emitters because of the indirect nature of their fundamental energy bandgap. This basic materials property has so far hindered the development of group-IV photonic active devices, including diode lasers, thereby significantly limiting our ability to integrate electronic and photonic functionalities at the chip level. Here we show that Ge nanomembranes (i.e., single-crystal sheets no more than a few tens of nanometers thick) can be used to overcome this materials limitation. Theoretical studies have predicted that tensile strain in Ge lowers the direct energy bandgap relative to the indirect one. We demonstrate that mechanically stressed nanomembranes allow for the introduction of sufficient biaxial tensile strain to transform Ge into a direct-bandgap material with strongly enhanced light-emission efficiency, capable of supporting population inversion as required for providing optical gain.