An ionic liquid (IL) is a salt in the liquid state that consists of a cation and an anion, one of which possesses an organic component. Because of their non-volatile property, these solvents have a high recovery rate, and, hence, they are considered as environment-friendly green solvents. It is necessary to study the detailed physicochemical properties of these liquids for designing and processing techniques and find suitable operating conditions for IL-based systems. In the present work, the flow behavior of aqueous solutions of an imidazolium-based IL, 1-methyl-3-octylimidazolium chloride, is investigated, where the dynamic viscosity measurements indicate non-Newtonian shear thickening behavior in the solutions. Polarizing optical microscopy shows that the pristine samples are isotropic and transform into anisotropic after shear. These shear thickened liquid crystalline samples change into an isotropic phase upon heating, which is quantified by the differential scanning calorimetry. The small angle x-ray scattering study revealed that the pristine isotropic cubic phase of spherical micelles distort into non-spherical micelles. This has provided the detailed structural evolution of mesoscopic aggregates of the IL in an aqueous solution and the corresponding viscoelastic property of the solution.