While shear flow is well known as the driver of instabilities such as the Kelvin-Helmholtz instability and inertial instability, it is shown here that in certain cases it inhibits eddy mixing. These are cases in which flow shear is significant, but insufficient to cause instability, and small scale turbulence is present due to another source. Using beta-place turbulence in a large scale, inertially stable jet as an illustration, it is shown that the straining by shear of turbulent eddies results in a reduction of cross-field transport scales and the corresponding eddy diffusivity. The mechanism entails the rapid stretching of eddies to their correlation length, with a resultant reduction of their lifetimes, amplitudes, and ability to transport across a constituent gradient. Dimensional scaling analysis is utilized to provide estimates of these modifications and the threshold condition for shear strength required for this effect. Numerical experiments are conducted for a large scale jet and small scale decaying beta-plane turbulence initialized in the jet flow. These experiments corroborate the results of the dimensional scaling analysis, indicating that transport is reduced in regions of enhanced shear.