Silicon is the dominant semiconductor for electronics, but there is now a growing need to integrate such components with optoelectronics for telecommunications and computer interconnections. Silicon-based optical modulators have recently been successfully demonstrated; but because the light modulation mechanisms in silicon are relatively weak, long (for example, several millimetres) devices or sophisticated high-quality-factor resonators have been necessary. Thin quantum-well structures made from III-V semiconductors such as GaAs, InP and their alloys exhibit the much stronger quantum-confined Stark effect (QCSE) mechanism, which allows modulator structures with only micrometres of optical path length. Such III-V materials are unfortunately difficult to integrate with silicon electronic devices. Germanium is routinely integrated with silicon in electronics, but previous silicon-germanium structures have also not shown strong modulation effects. Here we report the discovery of the QCSE, at room temperature, in thin germanium quantum-well structures grown on silicon. The QCSE here has strengths comparable to that in III-V materials. Its clarity and strength are particularly surprising because germanium is an indirect gap semiconductor; such semiconductors often display much weaker optical effects than direct gap materials (such as the III-V materials typically used for optoelectronics). This discovery is very promising for small, high-speed, low-power optical output devices fully compatible with silicon electronics manufacture.