The circadian clock controls behavior and physiology. Presently, there is clear evidence of a connection between this timing system and cancer development/progression. Moreover, circadian rhythm consideration in the therapeutic action of anticancer drugs can enhance the effectiveness of cancer therapy. Nanosized drug delivery systems (DDS) have been demonstrated to be suitable engineered platforms for drug targeted/sustained release. The investigation of the chronobiology-nanotechnology relationship, i.e., timing DDS performance according to a patient's circadian rhythm, may greatly improve cancer clinical outcomes. In the present work, we synthesized nanosystems based on an octa-arginine (R8)-modified poly(amidoamine) dendrimer conjugated with the anticancer drug paclitaxel (PTX), G4-PTX-R8, and its physicochemical properties were revealed to be appropriate for in vitro delivery. The influence of the circadian rhythm on its cellular internalization efficiency and potential therapeutic effect on human cervical cancer cells (HeLa) was studied. Cell-internalized PTX and caspase activity, as a measure of induced apoptosis, were monitored for six time points. Higher levels of PTX and caspase-3/9 were detected at T8, suggesting that the internalization of G4-PTX-R8 into HeLa cells and apoptosis are time-specific/-regulated phenomena. For a deeper understanding, the clock protein Bmal1-the main regulator of rhythmic activity, was silenced by Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) technology. Bmal1 silencing was revealed to have an impact on both PTX release and caspase activity, evidencing a potential role for circadian rhythm on drug delivery/therapeutic effect mediated by G4-PTX-R8.