All biomaterials initiate a tissue response when implanted in living tissues. Ultimately this reaction causes fibrous encapsulation and hence isolation of the material, leading to failure of the intended therapeutic effect of the implant. There has been extensive bioengineering research aimed at overcoming or delaying the onset of encapsulation. Nanotechnology has the potential to address this problem by virtue of the ability of some nanomaterials to modulate interactions with cells, thereby inducing specific biological responses to implanted foreign materials. To this effect in the present study, we have characterised the growth of fibroblasts on nano-structured sheets constituted by BaTiO3, a material extensively used in biomedical applications. We found that sheets of vertically aligned BaTiO3 nanotubes inhibit cell cycle progression - without impairing cell viability - of NIH-3T3 fibroblast cells. We postulate that the 3D organization of the material surface acts by increasing the availability of adhesion sites, promoting cell attachment and inhibition of cell proliferation. This finding could be of relevance for biomedical applications designed to prevent or minimize fibrous encasement by uncontrolled proliferation of fibroblastic cells with loss of material-tissue interface underpinning long-term function of implants.