We use a complete sample of 211 nearby (z<0.08), dwarf (10^8^M_{sun}_<M*<10^9.5^M_{sun}_) galaxies in low-density environments, to study their structural properties: effective radii (Re), effective surface brightnesses (<{mu}>_e_), and colour gradients. We explore these properties as a function of stellar mass and the three principal dwarf morphological types identified in a companion paper - early-type galaxies (ETGs), late-type galaxies (LTGs), and featureless systems. The median Re of LTGs and featureless galaxies are factors of ~2 and ~1.2 larger than the ETGs. While the median <{mu}>_e_ of the ETGs and LTGs is similar, the featureless class is ~1mag/arcsec^2^ fainter. Although they have similar median Re, the featureless and ETG classes differ significantly in their median <{mu}>_e_, suggesting that their evolution is different and that the featureless galaxies are not a subset of the ETGs. While massive ETGs typically exhibit negative or flat colour gradients, dwarf ETGs generally show positive colour gradients (bluer centres). The growth of ETGs therefore changes from being 'outside-in' to 'inside-out' as we move from the dwarf to the massive regime. The colour gradients of dwarf and massive LTGs are, however, similar. Around 46 per cent of dwarf ETGs show prominent, visually identifiable blue cores which extend out to ~1.5Re. Finally, compared to their non- interacting counterparts, interacting dwarfs are larger, bluer at all radii and exhibit similar median <{mu}>_e_, indicating that interactions typically enhance star formation across the entire galaxy.