As pulsars lose energy, primarily in the form of magnetic dipole radiation, their rotation slows down accordingly. For some pulsars, this spin-down is interrupted by occasional abrupt spin-up events known as glitches 1 . A glitch is hypothesized to be a catastrophic release of pinned vorticity 2 that provides an exchange of angular momentum between the superfluid outer core and the crust. This is manifested by a minute alteration in the rotation rate of the neutron star and its co-rotating magnetosphere, which is revealed by an abrupt change in the timing of observed radio pulses. Measurement of the flux density, polarization and single-pulse arrival times of the glitch with high time resolution may reveal the equation of state of the crustal superfluid, its drag-to-lift ratio and the parameters that describe its friction with the crust 3 . This has not hitherto been possible because glitch events happen unpredictably. Here we report single-pulse radio observations of a glitch in the Vela pulsar, which has a rotation frequency of 11.2 hertz. The glitch was detected on 2016 December 12 at 11:36 universal time, during continuous observations of the pulsar over a period of three years. We detected sudden changes in the pulse shape coincident with the glitch event: one pulse was unusually broad, the next pulse was missing (a 'null') and the following two pulses had unexpectedly low linear polarization. This sequence was followed by a 2.6-second interval during which pulses arrived later than usual, indicating that the glitch affects the magnetosphere.