The smallest unit of distance that we can actually measure is an Angstrom – this is 10 million times smaller than a millimetre. There are even smaller units than this, a femtometer (also known as a fermi) is 100,000 times smaller, and is about the size of an atomic nucleus.
Of course, distance is not the only unit of measurement. It is thought that a unit known as Planck time is the smallest measurement of time that will be possible. It is roughly equal to 10^−43 seconds