We investigate the shrinkage of a surface-grafted water-swollen hydrogel under shear flows of oils by laser scanning confocal microscopy. Interestingly, external shear flows of oil lead to linear dehydration and shrinkage of the hydrogel for all investigated flow conditions irrespective of the chemical nature of the hydrogel. The reason is that the finite solubility of water in oil removes water from the hydrogel continuously by diffusion. The flow advects the water-rich oil, as demonstrated by numerical solutions of the underlying convection-diffusion equation. In line with this hypothesis, shear does not cause gel shrinkage for water-saturated oils or non-solvents. The solubility of water in the oil will tune the dehydration dynamics.