Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of URu₂Si₂ has, despite relentless research efforts, kept its symmetry breaking element intangible. Here, we present a high-resolution x-ray diffraction study of the URu₂Si₂ crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold p_c ≈ 3 kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition T_HO = 17.5 K. For p > p_c, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures T_OR∼100 K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem.