Dynamics of fluctuations in critical fluids under shear flow is investigated when the system is suddenly brought from a thermodynamically stable state to an unstable state. Due to storong elongation effects of shear flow, fluctuations acquire increasingly two-dimensional character as time goes on. This is shown explicitly by applying to the Fokker-Planck equation for fluctuations time-dependent coarse-graining in the direction of flow. The correlations of fluctuations occuring at the different coarse-grained layers are discussed.