In this case, the phrase micro does mean the metric prefix 10^-6, but just "smaller than mRNA". The important unit in biology is nucleotides [1], which are the elements specifying the composition of proteins (loosely speaking, the "atoms of biology"). mRNA typically has on the order of thousands of nucleotides, whereas miRNAs have about 20 nucleotides. The physical size of miRNAs is actually ~3nm. [1]

[1] https://en.wikipedia.org/wiki/Nucleotide [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3500609/