Müller was the son of a saddler in Heidelberg. Along with Heinrich Boie and Heinrich Christian Macklot, he was sent by Coenraad Jacob Temminck to collect specimens in the East Indies. Here, he worked as an assistant for the Natuurkundige Commissie (Commission for Natural Sciences), an organization that he eventually became a member of.
Müller arrived in Batavia in 1826, then journeyed to New Guinea and Timor in 1828 aboard the Triton. Beginning in October 1828, he remained at the port city of Kupang, penetrating the interior of Timor during the following year. In 1831 he was stationed in Java, and later explored western Sumatra from 1833 to 1835.
Hermann Schlegel named Aspidomorphus muelleri (Müller’s crown snake) and Sphenomorphus muelleri (Müller's forest skink) in 1837, and Typhlops muelleri (Müller's blind snake) in 1839, all in honor of Salomon Müller. Similarly André Marie Constant Duméril, Gabriel Bibron and Auguste Duméril named Lycodon muelleri (Java wolf snake) in 1854 in honor of Müller.
- Reizen en onderzoekingen in Sumatra, gedaan op last der Nederlandsche Indische regering, tusschen de jaren 1833 en 1838, 1855.
- Reizen en onderzoekingen in den Indischen archipel, gedaan op last der Nederlandsche Indische regering, tusschen de jaren 1828 en 1836, 1857.
- Nationaal Herbarium Nederland (biography).
- Gert Jan Bestebreurtje Rare Books.
- Reptile Database Aspidomorphus muelleri.
- Beolens B, Watkins M, Grayson M. 2011. The Eponym Dictionary of Reptiles. Baltimore: Johns Hopkins University Press. xiii + 296 pp. ISBN 978-1-4214-0135-5. ("Mueller, S.", p. 184).
- OCLC Classify (publications).
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