We study the sizes of galaxies in the Epoch of Reionization using a sample of similar to 100 000 galaxies from the BLUETIDES cosmological hydrodynamical simulation from z = 7 to 11. We measure the galaxy sizes from stellar mass and luminosity maps, defining the effective radius as the minimum radius that could enclose the pixels containing 50 per cent of the total mass/light in the image. We find an inverse relationship between stellar mass and effective half-mass radius, suggesting that the most massive galaxies are more compact and dense than lower mass galaxies, which have flatter mass distributions. We find a mildly negative relation between intrinsic far-ultraviolet luminosity and size, while we find a positive size-luminosity relation when measured from dust-attenuated images. This suggests that dust is the predominant cause of the observed positive size-luminosity relation, with dust preferentially attenuating bright sightlines resulting in a flatter emission profile and thus larger measured effective radii. We study the size-luminosity relation across the rest-frame ultraviolet and optical, and find that the slope decreases at longer wavelengths; this is a consequence of the relation being caused by dust, which produces less attenuation at longer wavelengths. We find that the far-ultraviolet size-luminosity relation shows mild evolution from z = 7 to 11, and galaxy size evolves with redshift as R proportional to (1 + z)(-m), where m = 0.662 +/- 0.009. Finally, we investigate the sizes of z = 7 quasar host galaxies, and find that while the intrinsic sizes of quasar hosts are small relative to the overall galaxy sample, they have comparable sizes when measured from dust-attenuated images.