Measurements indicate that surprisingly small charge moment changes of similar to 200 C km in positive cloud-to-ground lightning discharges (+CGs) can initiate middle atmospheric gas discharges termed sprites. In the present work a plasma fluid model is used to demonstrate that for spherically symmetric initial electron density inhomogeneities, the initiation of sprites by such small charge moment changes is only possible when the ionospheric D-region electron density profile is characterized by a reference altitude h' greater than 90 km. Vertically elongated inhomogeneities are found to be more favorable for sprite initiation, which is consistent with recently published studies. It is calculated that for the same ionospheric conditions (i.e., inhomogeneities and h' values) that lead to initiation of sprites by +CGs associated with similar to 200 C km charge moment changes, the minimum charge moment change required for initiation of sprites by -CGs is 300 C km. Citation: Qin, J., S. Celestin, and V. P. Pasko (2012), Minimum charge moment change in positive and negative cloud to ground lightning discharges producing sprites, Geophys. Res. Lett., 39, L22801, doi: 10.1029/2012GL053951.