Fibre materials span a broad range of applications ranging from simple textile yarns to complex modern fibre-optic communication systems. Throughout their history, a key premise has remained essentially unchanged: fibres are static devices, incapable of controllably changing their properties over a wide range of frequencies. A number of approaches to realizing time-dependent variations in fibres have emerged, including refractive index modulation, nonlinear optical mechanisms in silica glass fibres and electroactively modulated polymer fibres. These approaches have been limited primarily because of the inert nature of traditional glassy fibre materials. Here we report the composition of a phase internal to a composite fibre structure that is simultaneously crystalline and non-centrosymmetric. A ferroelectric polymer layer of 30 mum thickness is spatially confined and electrically contacted by internal viscous electrodes and encapsulated in an insulating polymer cladding hundreds of micrometres in diameter. The structure is thermally drawn in its entirety from a macroscopic preform, yielding tens of metres of piezoelectric fibre. The fibres show a piezoelectric response and acoustic transduction from kilohertz to megahertz frequencies. A single-fibre electrically driven device containing a high-quality-factor Fabry-Perot optical resonator and a piezoelectric transducer is fabricated and measured.