There is some evidence that non-photoactivated psoralens may be active against breast and colon tumor cells. Therefore, we evaluated the antiproliferative, proapoptotic, and anti-migrative effect of 5-methoxypsoralen (5-MOP) isolated from Peucedanum tauricum MB fruits in human colorectal adenocarcinoma (HT-29 and SW620), osteosarcoma (Saos-2 and HOS), and multiple myeloma (RPMI8226 and U266). Dose- and cell-line-dependent effects of 5-MOP on viability and proliferation were observed, with the strongest inhibitory effect against Saos-2 and a moderate effect against the HOS, HT-29, and SW620 cells. Multiple myeloma showed low sensitivity. The high viability of human normal cell cultures (HSF and hFOB) in a wide range of 5-MOP concentrations tested (6.25–100 µM) was confirmed. Moreover, the migration of treated Saos-2, SW620, and HT-29 cell lines was impaired, as indicated via a wound healing assay. Flow cytometry analysis conducted on Saos-2 cells revealed the ability of 5-MOP to block the cell cycle in the G2 phase and trigger apoptosis, which was accompanied by a loss of mitochondrial membrane potential, caspases (-9 and -3) activation, the altered expression of the Bax and Bcl-2 proteins, and decreased AKT phosphorylation. This is the first report evaluating the antiproliferative and antimigratory impact of non-UV-activated bergapten on the abovementioned (except for HT-29) tumor cells, which provides new data on the potential role of 5-MOP in inhibiting the growth of various types of therapeutic-resistant cancers.