We studied a delay differential equations model for the population dynamics of diabetes during pregnancy. We considered four variables, namely women who are non-diabetic, women who are diabetic, women with gestational diabetes, and women with gestational diabetes and diabetes-related complications. We investigated the stability analysis of the equilibrium point by deriving of the transcendental characteristic equation. The numerical diagrams are visualized to verify the theoretical results. We further investigated the sensitivity analysis with respect to the equilibrium point. The normalized forward sensitivity indices suggested the critical and sensitive model inputs that capable of being handled to tackle the problems of diabetes during pregnancy.