The origin of the pseudogap region below a temperature T* is at the heart of the mysteries of cuprate high-temperature superconductors. Unusual properties of the pseudogap phase, such as broken time-reversal and inversion symmetry are observed in several symmetry-sensitive experiments: polarized neutron diffraction, optical birefringence, dichroic angle-resolved photoemission spectroscopy, second harmonic generation, and polar Kerr effect. These properties suggest that the pseudogap region is a genuine thermodynamic phase and are predicted by theories invoking ordered loop currents or other forms of intra-unit-cell (IUC) magnetic order. However, muon spin rotation (μSR) and nuclear magnetic resonance (NMR) experiments do not see the static local fields expected for magnetic order, leaving room for skepticism. The magnetic resonance probes have much longer time scales, however, over which local fields could be averaged by fluctuations. The observable effect of the fluctuations in magnetic resonance is then dynamic relaxation. We have measured dynamic muon spin relaxation rates in single crystals of YBa2Cu3O y (6.72 < y < 6.95) and have discovered "slow" fluctuating magnetic fields with magnitudes and fluctuation rates of the expected orders of magnitude that set in consistently at temperatures Tmag ≈ T*. The absence of any static field (to which μSR would be linearly sensitive) is consistent with the finite correlation length from neutron diffraction. Equally important, these fluctuations exhibit the critical slowing down at Tmag expected near a time-reversal symmetry breaking transition. Our results explain the absence of static magnetism and provide support for the existence of IUC magnetic order in the pseudogap phase.