Magnon-mediated angular-momentum flow in antiferromagnets may become a design element for energy-efficient, low-dissipation and high-speed spintronic devices1,2. Owing to their low energy dissipation, antiferromagnetic magnons can propagate over micrometre distances3. However, direct observation of their high-speed propagation has been elusive due to the lack of sufficiently fast probes2. Here we measure the antiferromagnetic magnon propagation in the time domain at the nanoscale (≤50 nm) with optical-driven terahertz emission. In non-magnetic-Bi2Te3/antiferromagnetic-insulator-NiO/ferromagnetic-Co trilayers, we observe a magnon velocity of ~650 km s–1 in the NiO layer. This velocity far exceeds previous estimations of the maximum magnon group velocity of ~40 km s–1, which were based on the magnon dispersion measurements of NiO using inelastic neutron scattering4,5. Our theory suggests that for magnon propagation at the nanoscale, a finite damping makes the dispersion anomalous for small magnon wavenumbers and yields a superluminal-like magnon velocity. Given the generality of finite dissipation in materials, our results strengthen the prospects of ultrafast nanodevices using antiferromagnetic magnons.