Atomically thin two-dimensional crystals have revolutionized materials science1, 2, 3. In particular, monolayer transition metal dichalcogenides promise novel optoelectronic applications, owing to their direct energy gaps in the optical range4, 5, 6, 7, 8, 9. Their electronic and optical properties are dominated by Coulomb-bound electron–hole pairs called excitons10, 11, 12, 13, 14, 15, 16, 17, 18, whose unusual internal structure13, symmetry15, 16, 17, many-body effects18 and dynamics have been vividly discussed. Here we report the first direct experimental access to all 1s A excitons, regardless of momentum—inside and outside the radiative cone—in single-layer WSe2. Phase-locked mid-infrared pulses reveal the internal orbital 1s–2p resonance, which is highly sensitive to the shape of the excitonic envelope functions and provides accurate transition energies, oscillator strengths, densities and linewidths. Remarkably, the observed decay dynamics indicates an ultrafast radiative annihilation of small-momentum excitons within 150 fs, whereas Auger recombination prevails for optically dark states. The results provide a comprehensive view of excitons and introduce a new degree of freedom for quantum control, optoelectronics and valleytronics of dichalcogenide monolayers19, 20, 21, 22, 23, 24.