We introduce a lateral atomic force microscopy (AFM) method to measure the hydrodynamic drag force acting on a microscopic emulsion droplet moving parallel to a flat surface. A tetradecane oil droplet formed in an aqueous solution of sodium dodecylsulfate was attached to a V-shaped atomic force microscopy cantilever, and lateral hydrodynamic interactions between the droplet and a flat glass surface were measured using a range of scanning velocities. The droplet was positioned either far from the oscillating surface or was pressed to the surface under a constant applied load. These measurements demonstrate the feasibility of using AFM to study lateral hydrodynamic interactions and lubricity between soft matter materials relevant to a large number of applications in areas as diverse as flavor delivery in foods to the applications of emulsions or emollients in personal care products.