  We show that a class of $\mathcal{PT}$ symmetric non-Hermitian Hamiltonians
realizing the Yang-Lee edge singularity exhibits an entanglement transition in
the long-time steady state evolved under the Hamiltonian. Such a transition is
induced by a level crossing triggered by the critical point associated with the
Yang-Lee singularity and hence is first-order in nature. At the transition, the
entanglement entropy of the steady state jumps discontinuously from a
volume-law to an area-law scaling. We exemplify this mechanism using a
one-dimensional transverse field Ising model with additional imaginary fields,
as well as the spin-1 Blume-Capel model and the three-state Potts model. We
further make a connection to the forced-measurement induced entanglement
transition in a Floquet non-unitary circuit subject to continuous measurements
followed by post-selections. Our results demonstrate a new mechanism for
entanglement transitions in non-Hermitian systems harboring a critical point.
