We present the first high spatial and spectral resolution observations of the circumstellar envelope (CSE) of a B[e] supergiant (CPD−57 • 2874), performed with the Very Large Telescope Interferometer (VLTI). Spectra, visibilities and closure phase were obtained using the beam-combiner instruments AMBER (near-IR interferometry with three 8.3 m Unit Telescopes or UTs) and MIDI (mid-IR interferometry with two UTs). The interferometric observations of the CSE are well fitted by an elliptical Gaussian model with FWHM diameters varying linearly with wavelength. Typical diameters measured are 1.8 × 3.4 mas or 4.5 × 8.5 AU (adopting a distance of 2.5 kpc) at 2.2 µm, and 12 × 15 mas or 30 × 38 AU at 12 µm. The size of the region emitting the Brγ flux is 2.8 × 5.2 mas or 7.0 × 13.0 AU. The major-axis position angle of the elongated CSE in the mid-IR (144 •) agrees well with previous polarimetric data, hinting that the hot-dust emission originates in a disk-like structure. In addition to the interferometric observations we also present new optical (UBVR c I c) and near-IR (JHKL) broadband photometric observations of CPD−57 • 2874. Our spectro-interferometric VLTI observations and data analysis support the non-spherical CSE paradigm for B[e] supergiants.