Hoppe, a merchant's son from Vilsen, Hanover, began his career as a pharmacy apprentice in Celle, and subsequently was an assistant pharmacist in Hamburg, Halle, Wolfenbüttel and Regensburg.

From 1792 onwards, he studied medicine and natural sciences at the University of Erlangen, and following graduation returned to Regensburg as a physician.

With bryologist Christian Friedrich Hornschuch (1793–1850), he published a treatise involving an extended scientific journey to the Adriatic coast and the mountains of Carinthia and Tyrol, called "Tagebuch einer Botanischen Reise nach den Küsten des Adriatischen Meeres und den Gebirgen von Kärnten, Tirol und Salzburg 1799".

He explored the region around Heiligenblut and the Grossglockner several times, where he found and described Eriophorum scheuchzeri, Sesleria ovata, Polytrichum sexangulare, Pedicularis asplenifolia, and Braya alpina.

Among his written efforts are a work on the flora of Regensburg, titled "Ectypa plantarum ratisbonensium" (1787–1793), and "Caricologia Germanica" (1835), a book of German caricology that he published with engraver Jacob Sturm (1771–1848).