Judith Rodriguez grew up in Brisbane, where she was educated at Brisbane Girls Grammar School and gained a Bachelor of Arts degree at the University of Queensland. She then travelled to England, graduating from Cambridge University in 1965 with a Master of Arts degree. In 1964 she married Colombian Fabio Rodriguez. They lived in England until 1968, then returned to Australia. Judith Rodriguez joined the English Department of La Trobe University, Victoria, in 1969 and remained there until 1985. During this period her marriage to Rodriguez ended. She had a number of appointments at academic institutions, including a period in 1986 as writer-in-residence at Rollins College, Florida (commemorated in Floridian Poems (1986)). In 1989 she accepted a lectureship in writing at Victoria College, which in 1993 became part of Deakin University. She was appointed Area Coordinator in Professional Writing at Deakin University in 1998, and retired from this position in 2003.
As well as being a poet and academic, Judith Rodriguez has also filled the role of editor in a number of enterprises. She was poetry editor of Meanjin from 1979 to 1982, and edited the Penguin Australian Poetry Series from 1988 to 1997. She has also been president of the Australian Association for Literary Translation, and was advisory editor (with Thomas Shapcott (q.v.)) for Swedish Poets in Translation (1985) and I Sogni Cantano l'Alba : Poesia Australiana Contemporanea (1946-1988) (1988). Her translations include Three Screenplays by Federico Fellini , translated from the Italian in 1970, as well as the novella Your Good Colombian Friend, translated from the Spanish in 1995.
In 1974, 1978 and 1983 Rodriguez was a Fellow of the Arts Council of Australia. She collaborated with Moya Henderson on the opera Lindy, premiered in 2003 at the Sydney Opera House, and with Robyn Archer (q.v.) on the play Poor Johanna, produced in Adelaide in 1994. Her linocuts appear in several of her poetry collections, and have been exhibited. She also wrote the text, with Vicki Pauli, for the art book Noela Hjorth (1984). She has been an active member of the Australian Society of Authors, International P.E.N., and Friends of the A.B.C.