Wavelength-scale periodic microstructuring dramatically alters the optical properties of materials. In this letter, we explore stimulated Brillouin scattering in PCFs with subwavelength-scale solid silica glass cores. The large refractive-index difference between air and glass allows much tighter confinement of light than is possible in all-solid single-mode glass optical fibres made using conventional techniques. When the silica-air PCF has a core diameter of around 70% of the vacuum wavelength of the launched laser light, we find that the spontaneous Brillouin signal develops a highly unusual multi-peaked spectrum with Stokes frequency shifts in the 10-GHz range. We attribute these peaks to several families of guided acoustic modes each with different proportions of longitudinal and shear strain, strongly localized to the core. At the same time, the threshold power for stimulated Brillouin scattering increases fivefold. The results show that Brillouin scattering is strongly affected by nanoscale microstructuring, opening new opportunities for controlling light—sound interactions in optical fibres.