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We report constraints on the parameters of Yukawa-type corrections toNewtonian gravity from measurements of the gradient of the Casimir force in theconfiguration of an Au-coated sphere above a Si plate covered with corrugationsof trapezoidal shape. For this purpose, the exact expression for the gradientof Yukawa force in the experimental configuration is derived and compared withthat obtained using the proximity force approximation. The reported constraintsare of almost the same strength as those found previously from severaldifferent experiments on the Casimir force and extend over a wide interactionrange from 30 to 1260\,nm. It is discussed how to make them stronger byreplacing the material of the plate.

Constraints on non-Newtonian gravity from measuring the Casimir force in a configuration with nanoscale rectangular corrugations