Finkelberg began teaching in 1987 at the Hebrew University and from 1991 taught at Tel Aviv University. While there, she was the recipient of the 1991 Gildersleeve Prize from the Johns Hopkins University Press for the best article published in the American Journal of Philology. A few years later, while still teaching at Tel Aviv University, Finkelberg published The Birth of Literary Fiction in Ancient Greece in 1998. From 1999–2000, Finkelberg studied as a Visiting Fellow at All Souls College, Oxford where she began to craft her future book Greeks and Pre-Greeks: Aegean Prehistory and Greek Heroic Tradition. In the early 2000s, Finkelberg collaborated with Guy Stroumsa at the Institute for Advanced Studies at the Hebrew University of Jerusalem to research "Mechanisms of Canon-Making in Ancient Societies." These efforts would later come into fruition in 2003, with their book Homer, the Bible, and Beyond: Literary and Religious Canons in the Ancient World. Despite this, Finkelberg still wrote about linguistics. In an article from 2001, Finkelberg demonstrated that there was a "high degree of correspondence between the phonological and morphological system of Minoan and that of Lycian" and proposed that "the language of Linear A is either the direct ancestor of Lycian or a closely related idiom." Beginning in 2002, Finkelberg headed the Department of Classics at Tel Aviv University until 2006. In 2005, Finkelberg became a member of the Israel Academy of Sciences and Humanities. That same year, she also published Greeks and Pre-Greeks: Aegean Prehistory and Greek Heroic Tradition. From 2006 – 07, Finkelberg was a Member of the Institute for Advanced Study at Princeton University. While there, she received funding to study the impact of Homeric poems. In 2011, she was elected president of the Israel Society for the Promotion of Classical Studies and was selected to sit on the Committee for the Evaluation of Archaeology Study Programs at Ben-Gurion University of the Negev. The following year, Finkelberg edited the first Homer Encyclopedia, which was considered the first comprehensive reference work on the Greek poet Homer. She was also the 2012 Recipient of the Rothschild Prize in the Humanities. In 2013, Finkelberg sat on the Dan David PrizeReview Committee for Classics, the Modern Legacy of the Ancient World. She was also an International Visiting Research Scholar at the University of British Columbia. In 2016, Finkelberg stepped down as president of the Israel Society for the Promotion of Classical Studies. She retired from teaching in 2017.
