Terahertz (THz) waves, known as non-ionizing radiation owing to their low photon energies, can actually ionize atoms and molecules when a sufficiently large number of THz photons are concentrated in time and space. Here, we demonstrate the generation of ionizing, multicycle, 15-THz waves emitted from large-area lithium niobate crystals via phase-matched optical rectification of 150-terawatt laser pulses. A complete characterization of the generated THz waves in energy, pulse duration, and focal spot size shows that the field strength can reach up to 260 megavolts per centimeter. In particular, a single-shot THz interferometer is employed to measure the THz pulse duration and spectrum with complementary numerical simulations. Such intense THz pulses are irradiated onto various solid targets to demonstrate THz-induced tunneling ionization and plasma formation. This study also discusses the potential of nonperturbative THz-driven ionization in gases, which will open up new opportunities, including nonlinear and relativistic THz physics in plasma.