The Etruscan shrew, also known as the Etruscan pygmy shrew or the white-toothed pygmy shrew, is the smallest known extant mammal by mass, weighing only about 1.8 grams (0.063 oz) on average.

It is characterized by very rapid movements and a fast metabolism, eating about 1.5–2 times its own body weight per day. It feeds on various small vertebrates and invertebrates, mostly insects, and can hunt individuals of the same size as itself. These shrews prefer warm and damp climates and are widely distributed in the belt between 10° and 30°N latitude stretching from Europe and North Africa up to Malaysia.

The pygmy jerboa's weight is about 3g and is found in Pakistan and Afghanistan.

The American shrew mole's weight is about 10g and is found in northwestern USA.

The long-tailed planigale's weight is about 4.3g and is found in Australia

More Info: en.wikipedia.org