Context. The evolution of galaxies depends on their interaction with the surrounding environment. Ultra-diffuse galaxies (UDGs) have been found in large numbers in clusters. We detected a few star-forming blobs in the VESTIGE survey, located at ∼5 kpc from a UDG, namely NGVS 3543, in association with an HI gas cloud AGC 226178, suggesting a recent interaction between this low-surface-brightness system and the surrounding cluster environment. Aims. We use a complete set of multi-frequency data including deep optical, UV, and narrow-band Hα imaging and HI data to understand the formation process that gave birth to this peculiar system. Methods. For this purpose, we measured (i) the multi-wavelength radial surface brightness profiles of NGVS 3543 and compared them to the predictions of spectro-photometric models of galaxy evolution in rich clusters; and (ii) the aperture photometry of the blue regions in the vicinity of NGVS 3543 in order to determine their age and stellar mass. Results. Comparisons of the observations with evolutionary models indicate that NGVS 3543 has undergone a ram-pressure stripping that peaked ∼100 Myr ago, transforming a blue gas-rich UDG into a red gas-poor UDG. Star formation has taken place in the ram pressure stripped gas, the mass of which is ∼108 M⊙, forming star complexes with a typical age of ∼20 Myr and a stellar mass of ∼104 M⊙. Conclusions. These results suggest that we are observing for the first time the ongoing transformation of a gas-rich UDG into a red and quiescent UDG under the effect of a ram-pressure stripping event. The same process could explain the lack of star-forming UDGs in rich environments observed in several nearby clusters.