Precise time-dependent measurements of the Z = 2 component in the cosmic radiation provide crucial information about the propagation of charged particles through the heliosphere. The PAMELA experiment, with its long flight duration (15th June 2006 - 23rd January 2016) and the low energy threshold (80 MeV/n) is an ideal detector for cosmic ray solar modulation studies. In this paper, the helium nuclei spectra measured by the PAMELA instrument from July 2006 to December 2009 over a Carrington rotation time basis are presented. A state-of-the-art three-dimensional model for cosmic-ray propagation inside the heliosphere was used to interpret the time-dependent measured fluxes. Proton-to-helium flux ratio time profiles at various rigidities are also presented in order to study any features which could result from the different masses and local interstellar spectra shapes.