Research efforts are placing an ever increasing emphasis on identifying signal transduction pathways related to the chemopreventive activity of curcumin. Its anticarcinogenic effects are presumably mediated by the regulation of signaling cascades, including nuclear factor κB (NF-κB), activator protein 1 (AP-1), and mitogen-activated protein kinases (MAPK). By modulating signal transduction pathways, curcumin induces apoptosis in malignant cells, thus inhibiting cancer development and progression. Due to the lack of mechanistic insight in the scientific literature, we developed a novel inverse molecular docking protocol based on the CANDOCK algorithm. For the first time, we performed inverse molecular docking of curcumin into a collection of 13,553 available human protein structures from the Protein Data Bank resulting in prioritized target proteins of curcumin. Our predictions were in agreement with the scientific literature and confirmed that curcumin binds to folate receptor β, DNA (cytosine-5)-methyltransferase 3A, metalloproteinase-2, mitogen-activated protein kinase 9, epidermal growth factor receptor and apoptosis-inducing factor 1. We also identified new potential protein targets of curcumin, namely deoxycytidine kinase, NAD-dependent protein deacetylase sirtuin-1 and -2, ecto-5′-nucleotidase, core histone macro-H2A.1, tyrosine-protein phosphatase non-receptor type 11, macrophage colony-stimulating factor 1 receptor, GTPase HRas, aflatoxin B1 aldehyde reductase member 3, aldo-keto reductase family 1 member C3, amiloride-sensitive amine oxidase, death-associated protein kinase 2 and tryptophan-tRNA ligase, that may all play a crucial role in its observed anticancer effects. Moreover, our inverse docking results showed that curcumin potentially binds also to the proteins cAMP-specific 3′,5′-cyclic phosphodiesterase 4D and 17-β-hydroxysteroid dehydrogenase type 10, which provides a new explanation for its efficiency in the treatment of Alzheimer’s disease. We firmly believe that our computational results will complement and direct future experimental studies on curcumin’s anticancer activity as well as on its therapeutic effects against Alzheimer’s disease.