Supernova 1987A in the Large Magellanic Cloud is surrounded by an extended region of nebulosity likely to be composed of material ejected during the evolution of the progenitor star, and which has been subsequently illuminated by the supernova event itself. Recent Hubble Space Telescope (HST) images have revealed the presence of two large elliptical rings of emission on either side of the previously discovered inner ring. Here we present the results of numerical calculations which show that this effect can be achieved by frictional interaction of a low-mass binary companion with the wind of the progenitor star. During the red supergiant phase, the dense, slow wind is shaped into a `double-cone' structure which is then swept up into a pair of circular rings by the fast stellar wind as the progenitor evolves towards a blue supergiant. The drag on the companion star is sufficient to coalesce the binary within the lifetime of the red supergiant, leading to a common-envelope phase and the ejection of envelope material in the orbital plane. This material, when swept up by the fast wind, could explain the presence of the third, inner ring.