Context. A sample of low-mass Hα emission line sources at z ∼ 0.4 was studied in the context of the mass-metallicty relation (MZR) and its possible evolution. We drew our sample from the OSIRIS Tunable Emission Line Object (OTELO) survey, which exploits the red tunable filter of OSIRIS at the Gran Telescopio Canarias to perform a blind narrow-band spectral scan in a selected field of the Extended Groth Strip. We were able to directly measure emission line fluxes and equivalent widths from the analysis of OTELO pseudo-spectra. Aims. This study aims to explore the MZR in the very low-mass regime. Our sample reaches stellar masses (M_*) as low as 10^6.8 M_⊙, where 63% of the sample have M_* < 10⁹ M_⊙. We also explore the relation of the star formation rate (SFR) and specific SFR with M_* and gas-phase oxygen abundances, as well as the M_*-size relation and the morphological classification. Methods. The M_* were estimated using synthetic rest-frame colours. Using an χ² minimization method, we separated the contribution of [N II]λ6583 to the Hα emission lines. Using the N2 index, we separated active galactic nuclei from star-forming galaxies (SFGs) and estimated the gas metallicity. We studied the morphology of the sampled galaxies qualitatively (visually) and quantitatively (automatically) using high-resolution data from the Hubble Space Telescope-ACS. The physical size of the galaxies was derived from the morphological analysis using GALAPAGOS2/GALFIT, where we fit a single-Sérsic 2D model to each source. Results. We find no evidence for an MZR evolution from comparing our very low-mass sample with local SFGs from the Sloan Digital Sky Survey. Furthermore, the same is true for M_*-size and M_*-SFR relations, as we deduce from comparison with recent literature. Morphologically, our sample is mostly (63%) populated by late-type galaxies, with 13% of early-type sources. For the first time, we identify one possible candidate outlier in the MZR at z = 0.4. The stellar-mass, metallicity, colour, morphology, and SFR of this source suggest that it is compatible with a transitional dwarf galaxy.