The so-called proximity effect is the manifestation, across an interface, of the systematic competition between magnetic order and superconductivity. This phenomenon has been well documented and understood for conventional superconductors coupled with metallic ferromagnets; however it is still less known for oxide materials, where much higher critical temperatures are offered by copper oxide-based superconductors. Here we show that, even in the absence of direct Cu-O-Mn covalent bonding, the interfacial CuO2 planes of superconducting La(1.85)Sr(0.15)CuO(4) thin films develop weak ferromagnetism associated to the charge transfer of spin-polarised electrons from the La(0.66)Sr(0.33)MnO(3) ferromagnet. Theoretical modelling confirms that this effect is general to all cuprate/manganite heterostructures and the presence of direct bonding only affects the strength of the coupling. The Dzyaloshinskii-Moriya interaction, also at the origin of the weak ferromagnetism of bulk cuprates, propagates the magnetisation from the interface CuO2 planes into the superconductor, eventually depressing its critical temperature.