We report on the spread of [Fe/H] values in the massive Large Magellanic Cloud cluster NGC 1978, recently confirmed to harbor multiple populations of nearly the same age. We used accurate Stromgren photometry of carefully selected cluster red giant branch stars along with a high-dispersion spectroscopy-based calibration of the metallicity-sensitive index m1. Once we accounted for the photometry quality, assessed from extensive artificial star tests to trace the photometric uncertainties as a function of the position of the cluster's center as well as the stellar brightness, and those from the metallicity calibration, we found that NGC 1978 exhibits a small metallicity spread of 0.035 dex (±0.019-0.023), depending on whether stars with individual σ[Fe/H] <= 0.15 dex or those located in the cluster's outer areas are considered. Such a spread in [Fe/H] is consistent with a cluster formation model with self-enrichment, if mass loss higher than 90% due to stellar evolutionary and galactic tidal effects is assumed. Nevertheless, scenarios in which the apparent [Fe/H] variation reflects CN abundance anomalies or less extreme mass-loss models with environmentally dependent self-enrichment should not be ruled out.