Diffusivities of the ionic surfactant aggregates with different aggregation numbers as well as self-diffusion coefficients of counterions and water molecules in the micellar solution at high total surfactant concentration have been computed and analysed within a molecular dynamics study. The study has been performed for aqueous solution of sodium dodecyl sulphate (SDS) at normal conditions using MDynaMix package with all-atom representation of SDS and water, with application of CHARMM36 force field and TIPS3P water model. The diffusivities of aggregates demonstrate the dependence on the aggregate size and are in general agreement with the results of dynamic light scattering experiments for micelle diffusivities at high surfactant concentrations. The diffusivities of sodium ions in micellar solutions corresponds to the results given by all-atom simulations of other authors.