Many natural micrometre-scale assemblies can be actuated to control their optical, transport and mechanical properties, yet such functionality is lacking in colloidal structures synthesized thus far. Here, we show with experiments and computer simulations that Janus ellipsoids can self-assemble into self-limiting one-dimensional fibres with shape-memory properties, and that the fibrillar assemblies can be actuated on application of an external alternating-current electric field. Actuation of the fibres occurs through a sliding mechanism that permits the rapid and reversible elongation and contraction of the Janus-ellipsoid chains by ~36% and that on long timescales leads to the generation of long, uniform self-assembled fibres. Colloidal-scale actuation might be useful in microrobotics and in applications of shape-memory materials.