Local Universe dwarf galaxies can serve as both cosmological and mass assembly probes. Deep surveys have enabled the study of these objects down to the low surface brightness (LSB) regime. In this paper, we estimate Euclid's dwarf detection capabilities as well as limits of its MERge processing function (MER pipeline), which is responsible for producing the stacked mosaics and final catalogues. To do this, we injected mock dwarf galaxies in a real Euclid Wide Survey (EWS) field in the VIS band and compared the input catalogue to the final MER catalogue. The mock dwarf galaxies were generated using simple Sérsic models with structural parameters (including size and surface brightness) drawn from observed dwarf galaxy catalogues. These simulations represent an idealised case in the sense they do not account for additional factors such as ellipticity, morphology, or crowding. To characterise the detected dwarfs, we used the mean surface brightness inside the effective radius SBe (in mag arcsec−2). The final MER catalogues achieve a completenesses of 91% for SBe ∈ [21, 24] and 54% for SBe ∈ [24, 28]. These numbers do not take into account possible contaminants, including confusion with background galaxies at the location of the dwarfs. After taking those effects into account, they respectively became 86% and 38%. The MER pipeline performs a final local background subtraction with a small mesh size, leading to a flux loss for galaxies with Re > 10″. By using the final MER mosaics and reinjecting this local background, we obtained an image in which we recover reliable photometric properties for objects under the arcminute scale. This background-reinjected product is thus suitable for the study of Local Universe dwarf galaxies. Euclid's data reduction pipeline serves as a test bed for other deep surveys, particularly regarding background subtraction methods, a key issue in LSB science.