In Galactic halo stars, sulphur has been shown to behave like other alpha-elements, but until now, no comprehensive studies have been done on this element in stars of other galaxies. Here, we use high-resolution ESO VLT/FLAMES/GIRAFFE spectra to determine sulphur abundances for 85 stars in the Sculptor dwarf spheroidal galaxy, covering the metallicity range -2.5 < or = Fe/H < or = -0.8. The abundances are derived from the S I triplet at 9213, 9228, and 9238 Angstrom. These lines have been shown to be sensitive to departure from local thermodynamic equilibrium, i.e. NLTE effects. Therefore, we present new NLTE corrections for a grid of stellar parameters covering those of the target stars. The NLTE-corrected sulphur abundances in Sculptor show the same behaviour as other alpha-elements in that galaxy (such as Mg, Si, and Ca). At lower metallicities (Fe/H <, ~ -2) the abundances are consistent with a plateau at S/Fe approximate + 0.16, similar to what is observed in the Galactic halo, S/Fe approximate + 0.2. With increasing Fe/H, the S/Fe ratio declines, reaching negative values at Fe/H > ~ -1.5. The sample also shows an increase in S/Mg with Fe/H, most probably because of enrichment from Type Ia supernovae.