Jenner was born in Alfriston, Sussex, England, the son of Thomas Jenner and his wife Sarah, née Ralf. He came to Victoria in 1850, and engaged in commercial pursuits at Geelong. Jenner held the office of president of the first reform league, established for the purpose of protecting native Industries.
Jenner represented the South Western Province in the Legislative Council for more than twenty years, being returned in March 1863 in opposition to Charles Griffith, and from 1875 to 1883 was Chairman of Committees. From September 1869 to April 1870 he acted as the representative of the John Alexander MacPherson Government in the Legislative Council, and subsequently discharged the same functions for the Charles Gavan Duffy Government. Jenner, who retired from the Council in July 1886, was a director of numerous local companies.
- Mennell, Philip (1892). " Jenner, Hon. Caleb Joshua". The Dictionary of Australasian Biography. London: Hutchinson & Co. Wikisource
- Beever, Margot. "Jenner, Caleb Joshua (1830–1890)". Australian Dictionary of Biography. Canberra: Australian National University. Retrieved 3 January 2014.
- "Jenner, Caleb Joshua". re-member: a database of all Victorian MPs since 1851. Parliament of Victoria. Retrieved 3 January 2014.