We report the results of our first-principles study based on density functional theory on the interaction of the nucleic acid base molecules adenine (A), cytosine (C), guanine (G), thymine (T), and uracil (U), with a single-walled carbon nanotube (CNT). Specifically, the focus is on the physisorption of base molecules on the outer wall of a (5,0) metallic CNT possessing one of the smallest diameters possible. Compared to CNTs with large diameters, the physisorption energy is found to be reduced in the high-curvature case. The base molecules exhibit significantly different interaction strengths, and the calculated binding energies follow the hierarchy G > A > T > C > U, which appears to be independent of the tube curvature. The stabilizing factor in the interaction between the base molecule and CNT is dominated by the molecular polarizability that allows a weakly attractive dispersion force to be induced between them. The present study provides an improved understanding of the role of the base sequence in deoxyribonucleic acid (DNA) or ribonucleic acid (RNA) on their interactions with carbon nanotubes of varying diameters.