We report the fabrication and proficient photocatalytic application of a series of heterojunction nanocomposites with cauliflower-like architecture synthesized out of copper oxide (CuO) and single-walled carbon nanotubes (SWCNTs). The photocatalysts with such a unique design were synthesized via facile recrystallization followed by calcination and were abbreviated as CuO-SWCNT-1, CuO-SWCNT-2, and CuO-SWCNT-3, representing the components and calcination time in hours. The photocatalytic efficiency of the fabricated nanocomposites was scanned by evaluating the decomposition of methylene blue (MB) dye under visible light irradiation. All samples of the as-synthesized nanocomposites were substantially effective photocatalysts for the photo-deterioration of MB solution. Moreover, CuO-SWCNT-3 revealed the best photocatalytic capability with 96% degradation of MB solution in 2 h under visible light irradiation. Pristine CuO nanocrystals generated through the same route and the SWCNTs were employed as controls, where the photocatalytic action of the nanocomposites was remarkably better than that of pristine CuO as well as SWCNTs. The recyclability of the photocatalysts was also explored, and the results asserted that the samples could be reused for three cycles without being altered in photocatalytic performance or morphology.