Subtropical ocean waters are susceptible to the occurrence of salt finger instability. The effect of salt fingers in modifying water mass properties may depend upon the ubiquitous presence of oceanic shear produced by internal wave motion. We present an experimental study of the buoyancy fluxes produced by sugar–salt fingers in the presence of a laminar shear flow. As is commonly done in the laboratory, sugar (the slower diffuser) was used as a proxy for salt, and salt (the faster diffuser compared to sugar) was used as a proxy for cold. Sugar–salt fingers, initially aligned vertically, were observed to tilt when a shear flow was imposed. A consistent decrease in the salt fluxes was measured as the Reynolds number (Re) was increased by increasing the shear velocity magnitude. Through regression analysis, the salt fluxes were found to depend upon the Reynolds number as Re−0.025, Re−0.1 and Re−0.34, for density ratio values (Rρ) equal to 1.2, 1.54 and 2.1 respectively. The salt fluxes produced by the sheared fingers were also found to decrease by one order of magnitude when Rρ increased from 1.2 to 2.1. A computation of the salt Nusselt number revealed that the finger fluxes approach molecular flux values when Rρ = 2.1 and Re ≃ 140.