The detection of infrared radiation enables night vision, health monitoring, optical communications and three-dimensional object recognition. Silicon is widely used in modern electronics, but its electronic bandgap prevents the detection of light at wavelengths longer than about 1,100 nanometres. It is therefore of interest to extend the performance of silicon photodetectors into the infrared spectrum, beyond the bandgap of silicon. Here we demonstrate a photovoltage field-effect transistor that uses silicon for charge transport, but is also sensitive to infrared light owing to the use of a quantum dot light absorber. The photovoltage generated at the interface between the silicon and the quantum dot, combined with the high transconductance provided by the silicon device, leads to high gain (more than 104 electrons per photon at 1,500 nanometres), fast time response (less than 10 microseconds) and a widely tunable spectral response. Our photovoltage field-effect transistor has a responsivity that is five orders of magnitude higher at a wavelength of 1,500 nanometres than that of previous infrared-sensitized silicon detectors. The sensitization is achieved using a room-temperature solution process and does not rely on traditional high-temperature epitaxial growth of semiconductors (such as is used for germanium and III-V semiconductors). Our results show that colloidal quantum dots can be used as an efficient platform for silicon-based infrared detection, competitive with state-of-the-art epitaxial semiconductors.