Two molecular modes of amphiphilic block copolymer-carbon nanotube interactions have been suggested in the literature, involving the adsorption of either individual block copolymer molecules or of multimolecular, spherical block copolymer micelles on the carbon nanotube. In both cases, the nature of stability imparted to the dispersion of nanotubes is kinetic, controlled by the steric barrier imposed by the adsorbed individual molecules or micelles. In this study we propose an alternate mode of molecular interaction, wherein the block copolymer molecules self-assemble around the nanotube to generate a thermodynamically stable aqueous dispersion. The possibility of such micellar solubilization of nanotubes is examined by constructing a phenomenological theory of nanotube solubilization. Illustrative calculations performed for polyethylene oxide- polypropylene oxide – polyethylene oxide (PEO-PPO-PEO) triblock copolymers show that they are capable of solubilizing carbon nanotubes in aqueous solutions. While the block copolymer molecules that spontaneously form cylindrical micelles are most likely to solubilize the nanotubes, other copolymers whose natural curvature is spherical or lamellar also are capable of forming cylindrical micelles around the nanotubes. Most interestingly, the solubilization is found to be size specific suggesting that this can be developed into a practical method to fractionate carbon nanotubes by size or chirality.