He studied at the universities of Jena, Leipzig and Tübingen, receiving his doctorate at the latter institution with a thesis on the instrumental case involving the Rigveda (1879).
By way of a recommendation from Ludwig Noiré, he continued his Oriental studies in Oxford under Max Müller.
From 1881 he spent the next two years in Herrnhut, where he studied Tibetology with Moravian missionary Heinrich August Jäschke.
In 1883 Wenzel published the second edition of Jäschke's "Tibetan grammar".
Later on, he returned to England, initially residing in Oxford, eventually settling in London.