Intermittency arising due to parametric noise has been observed across a variety of physical systems. A simple and generic approach for characterizing the onset of such intermittency in one-dimensional maps due to a periodic fluctuations of a system parameter is presented. Two mutually complementary conditions forthe onset of intermittency, with respect to the evolution during the two distinct phases constituting intermittent response are derived.We illustrate these ideas with numerical results from a noisy logistic map, with intermittencyabout a noise-free transcritical bifurcation and an aeroelastic system with intermittency about a noise-free Hopf bifurcation.