He was the father of geologist Carl Christian Gottsche (1859-1909). Gottsche was a leading authority of Hepaticae. With Christian Gottfried Daniel Nees von Esenbeck (1776-1858) and Johann Bernhard Wilhelm Lindenberg (1781-1851), he was author of Synopsis Hepaticarum (1844-1847), which was a landmark work in the field of hepaticology.
In 1881 he received an honorary doctorate in philosophy from the University of Kiel.
The botanical genus Gottschea in the family Schistochilaceae is named after him.