Single-molecule fluorescence techniques are key for a number of applications, including DNA sequencing, molecular and cell biology and early diagnosis. Unfortunately, observation of single molecules by diffraction-limited optics is restricted to detection volumes in the femtolitre range and requires pico- or nanomolar concentrations, far below the micromolar range where most biological reactions occur. This limitation can be overcome using plasmonic nanostructures, which enable the confinement of light down to nanoscale volumes. Although these nanoantennas enhance fluorescence brightness, large background signals and/or unspecific binding to the metallic surface have hampered the detection of individual fluorescent molecules in solution at high concentrations. Here we introduce a novel 'antenna-in-box' platform that is based on a gap-antenna inside a nanoaperture. This design combines fluorescent signal enhancement and background screening, offering high single-molecule sensitivity (fluorescence enhancement up to 1,100-fold and microsecond transit times) at micromolar sample concentrations and zeptolitre-range detection volumes. The antenna-in-box device can be optimized for single-molecule fluorescence studies at physiologically relevant concentrations, as we demonstrate using various biomolecules.