Blumberg was born in Brooklyn, New York, the son of Ida (Simonoff) and Meyer Blumberg, a Lawyer. He first attended the Orthodox Yeshivah of Flatbush for elementary school, where he learned to read and write in Hebrew, and to study the Bible and Jewish texts in their original language. (That school also had among its students a contemporary of Blumberg, Eric Kandel, who is another recipient of the Nobel Prize in Medicine.) Blumberg then attended Brooklyn's James Madison High School, a school that Blumberg described as having high academic standards, including many teachers with Ph.Ds. After moving to Far Rockaway, Queens, he transferred to Far Rockaway High School in the early 1940s, a school that also produced fellow laureates Burton Richter and Richard Feynman. Blumberg served as a U.S. Navy deck officer during World War II. He then attended Union College in Schenectady, New York and graduated from there with honors in 1946.

Throughout the 1950s, Blumberg traveled the world taking human blood samples, to study the genetic variations in human beings, focusing on the question of why some people contract a disease in a given environment, while others do not. In 1964, while studying "yellow jaundice" (hepatitis), he discovered a surface antigen for hepatitis B in the blood of an Australian aborigine. His work later demonstrated that the virus could cause liver cancer. Blumberg and his team were able to develop a screening test for the hepatitis B virus, to prevent its spread in blood donations, and developed a vaccine. Blumberg later freely distributed his vaccine patent in order to promote its distribution by drug companies. Deployment of the vaccine reduced the infection rate of hepatitis B in children in China from 15% to 1% in 10 years.

Originally entering the graduate program in mathematics at Columbia University, Blumberg switched to Medicine and enrolled at Columbia's College of Physicians and Surgeons, from which he received his MD in 1951. He remained at Columbia Presbyterian Medical Center for the next four years, first as an intern and then as a resident. He then moved to the University of Oxford and began graduate work in biochemistry at Balliol College, Oxford and earned his DPhil there in 1957. He later became the first American to be master at Balliol College, Oxford.

Blumberg became a member of the Institute of Cancer Research (ICR) of the Lankenau Hospital Research Institute in Philadelphia in 1964, which later joined the Fox Chase Cancer Center in 1974, and he held the rank of University Professor of Medicine and Anthropology at the University of Pennsylvania starting in 1977. Concurrently, he was Master of Balliol College from 1989 to 1994. He was elected a Fellow of the American Academy of Arts and Sciences in 1994. From 1999 to 2002, he was also Director of the NASA Astrobiology Institute at the Ames Research Center in Moffett Field, California.

In 1992, Blumberg participated in the founding of the Hepatitis B Foundation (HBF), a nonprofit organization dedicated to finding a cure for hepatitis B and improving the lives of those affected by hepatitis B worldwide. He served on the Scientific and Medical Advisory Board, and as its Distinguished Scholar from 1992 until his passing in 2011. Blumberg was a regular and inspirational presence at the Hepatitis Foundation, maintaining an office at The Foundation in Doylestown, Pennsylvania.

In 2001, Blumberg was named to the Library of Congress Scholars Council, a body of distinguished scholars that advises the Librarian of Congress. Blumberg served on the Council until his death.

In an interview with the New York Times in 2002 he stated that "[Saving lives] is what drew me to Medicine. There is, in Jewish thought, this idea that if you save a single life, you save the whole world".

In November 2004, Blumberg was named Chairman of the Scientific Advisory Board of United Therapeutics Corporation, a position he held until his death. As Chairman, he convened three "Conference[s] on Nanomedical and Telemedical Technology", as well as guiding the biotechnology company in the development of a broad-spectrum anti-viral Medicine.

Beginning in 2005, Blumberg also served as the President of the American Philosophical Society. He had first been elected to membership in the society in 1986.

In October 2010, Blumberg participated in the USA Science and Engineering Festival's Lunch with a Laureate program, in which middle and high school students of the Greater Washington D.C., Northern Virginia and Maryland area got to engage in an informal conversation with a Nobel Prize–winning scientist over a brown-bag lunch.

In 2011, in recognition of Blumberg's long professional and personal association with the Department of Biochemistry and the Glycobiology Institute, Oxford University established the Baruch Blumberg Professorship in Virology.