We provide manganese abundances (corrected for the effect of the hyperfine structure) for a large number of stars in the dwarf spheroidal galaxies Sculptor and Fornax, and for a smaller number in the Carina and Sextans dSph galaxies. Abundances had already been determined for a number of other elements in these galaxies, including α and iron-peak ones, which allowed us to build [Mn/Fe] and [Mn/α] versus [Fe/H] diagrams. The Mn abundances imply sub-solar [Mn/Fe] ratios for the stars in all four galaxies examined. In Sculptor, [Mn/Fe] stays roughly constant between [Fe/H] ~ -1.8 and -1.4 and decreases at higher iron abundance. In Fornax, [Mn/Fe] does not vary in any significant way with [Fe/H]. The relation between [Mn/α] and [Fe/H] for the dSph galaxies is clearly systematically offset from that for the Milky Way, which reflects the different star formation histories of the respective galaxies. The [Mn/α] behavior can be interpreted as a result of the metal-dependent Mn yields of Type II and Type Ia supernovae. We also computed chemical evolution models for star formation histories matching those determined empirically for Sculptor, Fornax, and Carina, and for the Mn yields of SNe Ia, which were assumed to be either constant or variable with metallicity. The observed [Mn/Fe] versus [Fe/H] relation in Sculptor, Fornax, and Carina can be reproduced only by the chemical evolution models that include a metallicity-dependent Mn yield from the SNe Ia. Based on observations made with the FLAMES-GIRAFFE multi-object spectrograph mounted on the Kuyen VLT telescope at ESO-Paranal Observatory (programs 171.B-0588, 074.B-0415 and 076.B-0146).Appendices are available in electronic form at http://www.aanda.org