Quiver Township is located in Mason County, Illinois, United States. As of the 2010 census, its population was 900 and it contained 517 housing units. It contains the census-designated place of Goofy Ridge.
Quiver Township took its name from Quiver Creek.
According to the 2010 census, the township has a total area of , of which (or 81.71%) is land and (or 18.29%) is water.