We discuss generalization of the Nambu-Goldstone theorem to open classical and quantum systems. For a Hamiltonian system, it is known that there appears a gapless excitation called the Nambu-Goldstone mode, when a global continuum symmetry is spontaneously broken. In this theorem, a conservation law plays an important role. In contrast, for an open system, the ordinary conservation law is violated because of interaction with environment. Nevertheless, we can define another symmetry using path integral formalism, whose Noether charge is different from ordinary one. We show that the Nambu-Goldstone mode appears when the symmetry is spontaneously broken in the open system. The NG mode is generally not propagating but dissipative. We also show the general form of the dispersion relation using Ward-Takahashi identity.  We discuss application to a real system such as an active matter system.