In the present investigation, the magnetohydrodynamic Falkner-Skan flow of tangent hyperbolic nanofluids over a stretching/shrinking wedge with variable suction, internal heat generation/absorption and chemical reaction with activation energy have been scrutinized. Nanofluid model is composed of “Brownian motion’’ and “Thermophoresis’’. Transformed non-dimensional coupled non-linear equations are solved by adopting the fourth-order R-K method along with the shooting technique. A comprehensive analysis of nanofluid velocity, the relative temperature, and its concentration profiles has been addressed. The major outcomes of the current study include that augmentation in the Weissenberg parameter, Hartmann number along with suction impede fluid flow and the shrinkage of the related boundary layer while internal heating develops an ascending thermal boundary layer for static and moving (stretching/shrinking) wedge. An increment in reaction rate undermines the nanoparticle concentration while that of activation energy exhibits a reverse trend.