Artificial multilayers offer unique opportunities for combining materials with antagonistic orders such as superconductivity and ferromagnetism and thus to realize novel quantum states. In particular, oxide multilayers enable the utilization of the high superconducting transition temperature of the cuprates and the versatile magnetic properties of the colossal-magnetoresistance manganites. However, apart from exploratory work, the in-depth investigation of their unusual properties has only just begun. Here we present neutron reflectometry measurements of a [Y(0.6)Pr(0.4)Ba(2)Cu(3)O(7) (10 nm)/La(2/3)Ca(1/3)MnO(3) (10 nm)](10) superlattice, which reveal a surprisingly large superconductivity-induced modulation of the vertical ferromagnetic magnetization profile. Most surprisingly, this modulation seems to involve the density rather than the orientation of the magnetization and is highly susceptible to the strain, which is transmitted from the SrTiO(3) substrate. We outline a possible explanation of this unusual superconductivity-induced phenomenon in terms of a phase separation between ferromagnetic and non-ferromagnetic nanodomains in the La(2/3)Ca(1/3)MnO(3) layers.