We report spatially resolved, spectrally dispersed N-band observations of the B[e] star Hen 3-1191 with the MIDI instrument of the Very Large Telescope Interferometer. The object is resolved with a 40 m baseline and has an equivalent uniform disc diameter ranging from 24 mas at 8 µm to 36 mas at 13 µm. The MIDI spectrum and visibilities show a curvature which can arise from a weak silicate feature in which the object appears ≈15% larger than in the continuum, but this could result from a change in the object's geometry within the band. We then model Hen's 3-1191 spectral energy distribution (.4−60 µm) and N-band visibilities. Because of the unknown nature of the object, we use a wide variety of models for objects with IR excesses. We find the observations to be consistent with a disc featuring an unusually high mass accretion and a large central gap almost void of matter, an excretion disc, and a binary made of two IR sources. We are unable to find a circumstellar shell model consistent with the data. We review the different hypotheses concerning the physical nature of the star and conclude that it is neither a Be supergiant nor a symbiotic star. However, we could not discriminate between the scenario of a young stellar object featuring an unusually strong FU Orionis-like outburst of mass accretion (4−250×10 −4 M /yr) and that of a protoplanetary nebula with an equatorial mass excretion rate > ∼ 4 × 10 −5 M /yr. In both cases, taking the additional presence of an envelope or wind into account would result in lower mass flows.