This is a significant jump for the university, which was ranked 51-75 last year.
Among the first 100 in math are other Israeli academic institutions, including the Technion, Tel Aviv University and the Weizmann Institute of Science.
The Weizmann Institute was also ranked 10 in computer sciences and 50 in chemistry. The Technion was ranked 51-75 while the Hebrew University was ranked 101-150 in chemistry.
In physics, only the Technion made it into the list of top 500 universities and was ranked 151-200.
In the field of economics, the Hebrew University was ranked at 46. In education, the University of Haifa was ranked 101-150, while Bar-Ilan University was ranked 151-200.
The Hebrew University was also ranked 51-75 in law and 76-100 in psychology.
The Shanghai Ranking is one of the two prominent academic rankings for universities in the world, with the other one being the London-based Times Higher Education.