New Salem Township is located in McDonough County, Illinois. As of the 2010 census, its population was 369 and it contained 168 housing units. It is Township 5 North, Range 1 West of the Fourth Principal Meridian. It contains the census-designated place of Adair.
According to the 2010 census, the township has a total area of , of which (or 99.97%) is land and (or 0.06%) is water.