Non-standard fields are assumed to be responsible for phenomena attributed to dark energy and dark matter. Being coupled to ordinary matter, these fields modify the masses and/or charges of the elementary particles, thereby violating the Weak Equivalence Principle. Thus, values of fundamental constants such as the proton-to-electron mass ratio, µ, and/or the fine structure constant, α, measured in different environment conditions can be used as probes for this coupling. Here we perform differential measurements of F = µα 2 to test a non-standard coupling in the Magellanic Clouds -dwarf galaxies where the overall mass budget is dominated by dark matter. The analysis is based on [C i] and CO lines observed with the Herschel Space Observatory. Since these lines have different sensitivities to changes in µ and α, the combined α and µ variations can be evaluated through the radial velocity offsets, ∆V , between the CO and [C i] lines. Averaging over nine positions in the Magellanic Clouds, we obtain ∆V = −0.02 ± 0.07 km s −1 , leading to |∆F/F | < 2 × 10 −7 (1σ), where ∆F/F = (F obs − F lab )/F lab . However, for one position observed with five times higher spectral resolution we find ∆V = −0.05 ± 0.02 km s −1 , resulting in ∆F/F = (−1.7 ± 0.7) × 10 −7 . Whether this offset is due to changes in the fundamental constants, due to chemical segregation in the emitting gas or merely due to Doppler noise requires further investigations.