We prove that $\mu$-constant deformations of generalized curves; that is, non-dicritical plane holomorphic foliations with no saddle-nodes in their desingularization, are equisingular. Furthermore, under the classical convenience assumption on the Newton diagram, we show that there exists an analytic family of coordinates preserving the Newton diagram throughout the deformation. Thus, we extend both the L\^{e}–Ramanujam theorem and Oka’s Newton stability to germs of plane holomorphic foliations.