John Muller studied at the South African College, Cape Town, from 1890 to 1895, passing the matriculation examination of the University of the Cape of Good Hope in 1892 and its Bachelor of Arts (BA) examination in mathematics and natural science in 1895. In August 1895 he started work as a temporary assistant analyst at the Government Analytical Laboratory in Cape Town, under C.F. Juritz*. Despite his junior position he reported on "Analysis of Colonial soils" in the Agricultural Journal of the Cape Colony (Vol. 8(24), pp. 621-624) later that year. His analyses of some 70 soil samples for calcium, potassium, phosphorus and nitrogen formed part of a systematic investigation of Cape soils initiated by Juritz. During 1896 he spent three months at the agricultural station at Halle, Germany, to study methods of analysis of soils and fertilisers. He was promoted to analyst in 1898.
In 1902 Muller was transferred to the Colonial Bacteriological Institute in Grahamstown and appointed as government analyst in charge of a new chemical laboratory for the Eastern Cape. Soon after his arrival he offered to re-label and arrange the mineral collection of the Albany Museum. During 1906 he became ill while on a visit to Europe and was absent from the laboratory for six months. Between 1903 and 1906 he was an examiner in chemistry for the University of the Cape of Good Hope and in 1914-1915 served as moderator for chemistry. In 1911 he returned to Cape Town as senior chemist in charge of the Government Analytical Laboratory. By that time he had been elected a Fellow of the Chemical Society, and was a member of the South African Association for the Advancement of Science.
Though his work was mainly of a routine nature some of his investigations were publishable. For example, in 1912 he reported on "The serum or precipitin test for blood and its practical application in medico-legal cases in the Cape Province" in the Report for 1912 of the South African Association for the Advancement of Science (pp. 77-84). Other papers by him, on "Yellowing of citrus trees" (1909) and "The chemical composition of milk in the eastern districts of the Cape Province" (1910), were published in the Proceedings of the Cape Chemical Society. He also wrote several articles for the Agricultural Journal of the Union of South Africa, for example, on the analysis of milk (1911), the analysis of wine (1913), and the composition and toxic properties of arenates (1913). In 1922 he was still active as a public and consulting chemist, submitting an analytical report to the Town Clerk of Malmesbury on the constituents of the town's thermal spring and its medicinal properties.