Membrane tension modulates the morphology of plasma-membrane tubular protrusions in cells but is difficult to measure. Here, we propose to use microscopy imaging to assess the membrane tension. We report direct measurement of membrane nanotube diameters with unprecedented resolution using stimulated emission depletion (STED) microscopy. For this purpose, we integrated an optical tweezers setup in a commercial microscope equipped for STED imaging and established micropipette aspiration of giant vesicles. Membrane nanotubes were pulled from the vesicles at specific membrane tension imposed by the aspiration pipet. Tube diameters calculated from the applied tension using the membrane curvature elasticity model are in excellent agreement with data measured directly with STED. Our approach can be extended to cellular membranes and will then allow us to estimate the mechanical membrane tension within the force-induced nanotubes.