Context. While Euclid is an ESA mission specifically designed to investigate the nature of dark energy and dark matter, the planned unprecedented combination of survey area (similar to 15000 deg(2)), spatial resolution, low sky-background, and depth also make Euclid an excellent space observatory for the study of the low surface brightness Universe. Scientific exploitation of the extended low surface brightness structures requires dedicated calibration procedures that are yet to be tested.

Aims. We investigate the capabilities of Euclid to detect extended low surface brightness structure by identifying and quantifying sky-background sources and stray-light contamination. We test the feasibility of generating sky flat-fields to reduce large-scale residual gradients in order to reveal the extended emission of galaxies observed in the Euclid survey.

Methods. We simulated a realistic set of Euclid/VIS observations, taking into account both instrumental and astronomical sources of contamination, including cosmic rays, stray-light, zodiacal light, interstellar medium, and the cosmic infrared background, while simulating the effects of background sources in the field of view.

Results. We demonstrate that a combination of calibration lamps, sky flats, and self-calibration would enable recovery of emission at a limiting surface brightness magnitude of mu(lim) = 29.5(-0.27)(+0.08) mag arcsec(-2) (3 sigma, 10 x 10 arcsec(2)) in theWide Survey, and it would reach regions deeper by 2 mag in the Deep Surveys.

Conclusions. Euclid/VIS has the potential to be an excellent low surface brightness observatory. Covering the gap between pixel-to-pixel calibration lamp flats and self-calibration observations for large scales, the application of sky flat-fielding will enhance the sensitivity of the VIS detector at scales larger than 1 '', up to the size of the field of view, enabling Euclid to detect extended surface brightness structures below mu(lim) = 31 mag arcsec(-2) and beyond.