Zika virus (ZIKV) is a mosquito‐transmitted flavivirus, linked to microcephaly and fetal death in humans. Here, we investigate whether host‐mediated RNA editing of adenosines (ADAR) plays a role in the molecular evolution of ZIKV. Using complete coding sequences for the ZIKV polyprotein, we show that potential ADAR substitutions are underrepresented at the ADAR‐resistant GA dinucleotides of both the positive and negative strands, that these changes are spatially and temporally clustered (as expected of ADAR editing) for three branches of the viral phylogeny, and that ADAR mutagenesis can be linked to its codon usage. Furthermore, resistant GA dinucleotides are enriched on the positive (but not negative) strand, indicating that the former is under stronger purifying selection than the latter. ADAR editing also affects the evolution of the rhabdovirus sigma. Our study now documents that host ADAR editing is a mutation and evolutionary force of positive‐ as well as negative‐strand RNA viruses.