Homogeneous nucleation of a new phase near an Ising-type critical point of another phase transition is studied. A scaling analysis shows that the free energy barrier to nucleation contains a singular term with the same scaling as the order parameter associated with the critical point. The total magnetization of the nucleus scales as the response function and so it diverges. Vapor-liquid critical points are in the Ising universality class and so our results imply that near such a critical point the number of molecules in a nucleus of another phase, such as a crystalline phase, diverges as the isothermal compressibility. The case where symmetry prevents coupling between the nucleus and the order parameter is also considered.