Hairy acronychia was first described in 1891 by Frederick Manson Bailey who gave it the name Melicope pubescens and published the description in the Botany Bulletin of the Department of Agriculture, Queensland from a collection from the Blackall Range. It gained its current binomial name in 1939 when reclassified by his grandson, Queensland Government Botanist Cyril Tenison White, in the Proceedings of the Royal Society of Queensland. The specific epithet pubescens means hairy, referring to the downy leaves.