Nova outbursts take place in binary star systems comprising a white dwarf and either a low-mass Sun-like star or, as in the case of the recurrent nova RS Ophiuchi, a red giant. Although the cause of these outbursts is known to be thermonuclear explosion of matter transferred from the companion onto the surface of the white dwarf, models of the previous (1985) outburst of RS Ophiuchi failed to adequately fit the X-ray evolution and there was controversy over a single-epoch high-resolution radio image, which suggested that the remnant was bipolar rather than spherical as modelled. Here we report the detection of spatially resolved structure in RS Ophiuchi from two weeks after its 12 February 2006 outburst. We track an expanding shock wave as it sweeps through the red giant wind, producing a remnant similar to that of a type II supernova but evolving over months rather than millennia. As in supernova remnants, the radio emission is non-thermal (synchrotron emission), but asymmetries and multiple emission components clearly demonstrate that contrary to the assumptions of spherical symmetry in models of the 1985 explosion, the ejection is jet-like, collimated by the central binary whose orientation on the sky can be determined from these observations.