The optical and near‐infrared (near‐IR) late‐time spectra of the under‐luminous Type Ia supernova 2003hv are analysed with a code that computes the nebular emission from a supernova nebula. Synthetic spectra based on the classical explosion model W7 are unable to reproduce the large Fe iii/Fe ii ratio and the low IR flux at ∼1 year after the explosion, although the optical spectrum of SN 2003hv is reproduced reasonably well for a supernova of luminosity intermediate between normal and subluminous (SN 1991bg‐like) ones. A possible solution is that the inner layers of the supernova ejecta (v≲ 8000 km s−1) contain less mass than predicted by classical explosion models like W7. If this inner region contains ∼ 0.5 M⊙ of material, as opposed to ∼ 0.9 M⊙ in Chandrasekhar‐mass models developed within the single‐degenerate scenario, the low density inhibits recombination, favouring the large Fe iii/Fe ii ratio observed in the optical, and decreases the flux in the [Fe ii] lines which dominate the IR spectrum. The most likely scenario may be an explosion of a sub‐Chandrasekhar‐mass white dwarf. Alternatively, the violent/dynamical merger of two white dwarfs with the combined mass exceeding the Chandrasekhar limit also shows a reduced inner density.