Two-level atoms coupled with single-mode cavity photons are predicted to exhibit a quantum phase transition when the coupling strength exceeds a critical value, entering a phase in which atomic polarization and the photonic field are finite even at zero temperature and without external driving. However, this phenomenon, the superradiant phase transition (SRPT), is forbidden by a no-go theorem due to the existence of the diamagnetic term in the Hamiltonian. Here, we present spectroscopic evidence for a magnonic SRPT in ErFeO3, where the role of the photonic mode (two-level atoms) in the photonic SRPT is played by an Fe3+ magnon mode (Er3+ spins). The absence of the diamagnetic term in the Fe3+--Er3+ exchange coupling ensures that the no-go theorem does not apply. Ultrabroadband terahertz and gigahertz magnetospectroscopy experiments revealed the signatures of the SRPT -- a kink and a softening, respectively, of two spin--magnon hybridized modes at the critical point. These results unambiguously demonstrate the long-sought SRPT in thermal equilibrium offered by the Dicke Hamiltonian. The approach of using exchange interactions to realize the magnonic SRPT provides insights into harnessing the powerful phenomena associated with photonic SRPTs and understanding condensed matter phases. Systems near this phase are expected to harbor large-scale entanglement and squeezing, which will potentially provide a route to a new class of quantum technologies.