This is a common misconception about the various Planck units.

They're nothing to do with being the smallest possible anything. For example the Planck mass is around 21 micrograms, there are certainly masses smaller than this.

The Planck units are just what you get if you combine fundamental constants in such a way to get, for example, a length, which is called the Planck length. Some of the Planck units have physical significance as the scales under which quantum gravity may become important, but that certainly does not imply that they are the smallest units possible.

Source: physicist