Batsch was born in Jena, Saxe-Weimar to George Lorenz Bratsch and Ernestine (nee Franke) Bratsch. He studied at the city school, and then had private tuition. He showed an aptitude for natural sciences, and so subsequently studied at the University of Jena (now known as the Friedrich Schiller University of Jena), entering in 1772 and obtaining his doctorate in 1781. Batsch was married in 1787 to Amalie Pfaundel. They had three children, Friedrich (born 1789), George Friedrich Karl (1792), and Karoline (1795). He died in 1802 after a short illness.
Batsch discovered almost 200 new species of mushrooms, including Clitocybe nebularis, Calocera cornea, Paxillus involutus, and Tapinella atrotomentosa. He was a recognised authority writing two books on the topic, Elenchus Fungorum (Discussion of Fungi, between 1783 and 1789), which is still highly rated today and Versuch einer Anleitung zur Kenntniss und Geschichte der Pflanzen (Attempt at Instruction in the Knowledge and History of Plants, between 1787 and 1788). Versuch einer Anleitung... looked into the nature of what we now know to be fungal diseases of plants (such as Dutch elm disease), but without realizing their origin.