Hencke was born in Driesen, Brandenburg (now Drezdenko, Poland). He volunteered in the Wars of Liberation (Befreiungskriege) for Prussia but was wounded at Lützen. Thereafter he served as post official at various places and finally was erected post master. After his retirement at age 45 for health reasons he lived in his city of birth where he served as city court judge.
He discovered two asteroids from his private observatory at #9, Kietz (now #43, Kietzerstraße), Driesen, by comparing star maps with the sky seen through his telescope. The first, 5 Astraea, is notable for being the first asteroid discovered after the long gap that followed the last of the original four, 4 Vesta, which was discovered in 1807. Other astronomers had abandoned their searches for more asteroids, convinced that there were only four. However, Hencke began searching in 1830, and fifteen years later met with success. He also worked on the improvement of star maps.
He died in Marienwerder (now Kwidzyn), then part of Prussia.