DNA-carbon nanotube hybrids (DNA-CN) are novel nanoscale materials that consist of single-wall carbon nanotubes (SWCN) coated with a self-assembled monolayer of single-stranded DNA (ssDNA). Recent experiments on DNA-CN have shown that this material offers a remarkable set of technologically useful properties such as facilitation of SWCN sorting, chemical sensing, and detection of DNA hybridization. Despite the importance of DNA-CN, a detailed understanding of its microscopic structure and physical properties is lacking. To address this, we have performed classical all-atom molecular dynamics (MD) simulations exploring the self-assembly mechanisms, structure, and energetic properties of this nanomaterial. MD reveals that SWCN induces ssDNA to undergo a spontaneous conformational change that enables the hybrid to self-assemble via the pi-pi stacking interaction between ssDNA bases and SWCN sidewall. ssDNA is observed to spontaneously wrap about SWCN into compact right- or left-handed helices within a few nanoseconds. Helical wrapping is driven by electrostatic and torsional interactions within the sugar-phosphate backbone that result in ssDNA wrapping from the 3' end to the 5' end.