A substantial influence of a magnetic field on the third-order nonlinear optical properties exhibited by aggregated networks of aligned carbon nanotubes (CNT) is reported by systematic measurements. A two-wave mixing was employed to explore and modulate the refractive index in the nanostructures in the nanosecond and picosecond regime. The presence of a magnetic field was able to modify the optical transmittance in the sample and the potentiality to generate structured light was proposed. Numerical simulations were conducted to analyze the magnetic field phenomena and the oscillations of the electric field in the studied sample. We discussed theoretical concepts, experimental methods, and computational tools employed to evaluate the third-order nonlinear optical properties of CNT in film form. Immediate applications of the system to modulate structured light can be contemplated.