NGC 4449 is a nearby Magellanic irregular starburst galaxy with a B-band absolute magnitude of -18 and a prominent, massive, intermediate-age nucleus at a distance from Earth of 3.8 megaparsecs (ref. 3). It is wreathed in an extraordinary neutral hydrogen (H I) complex, which includes rings, shells and a counter-rotating core, spanning ∼90 kiloparsecs (kpc; refs 1, 4). NGC 4449 is relatively isolated, although an interaction with its nearest known companion--the galaxy DDO 125, some 40 kpc to the south--has been proposed as being responsible for the complexity of its H I structure. Here we report the presence of a dwarf galaxy companion to NGC 4449, namely NGC 4449B. This companion has a V-band absolute magnitude of -13.4 and a half-light radius of 2.7 kpc, with a full extent of around 8 kpc. It is in a transient stage of tidal disruption, similar to that of the Sagittarius dwarf near the Milky Way. NGC 4449B exhibits a striking S-shaped morphology that has been predicted for disrupting galaxies but has hitherto been seen only in a dissolving globular cluster. We also detect an additional arc or disk ripple embedded in a two-component stellar halo, including a component extending twice as far as previously known, to about 20 kpc from the galaxy's centre.