Henry David Abraham graduated from Muhlenberg College in Allentown, Pennsylvania, and attended the Johns Hopkins School of Medicine on scholarship. Following medical school he served an internship in Pediatrics at the Johns Hopkins Hospital.  Subsequently he served as the medical advisor of the National Medical Audiovisual Center at the Communicable Disease Center, and in the Department of Community Medicine at the University of Arizona. He completed psychiatric training at the Massachusetts General Hospital, Harvard Medical School.

Over time he has served as Unit Chief of the Westboro State Hospital, Director of Psychiatric Research at the St. Elizabeth's Hospital in Boston, Director of Substance Abuse programs at the Tufts Medical Center, and Chief of the Alcohol and Drug Treatment programs at Butler Hospital, an affiliate of Brown University. He has also served as a consultant to the National Academy of Sciences, and as advisor for several revisions of the Diagnostic Manual (DSM) of the American Psychiatric Association. 

Writing honors include the IRIS, Peabody and Emmy Awards for Best Public Television Programs in 1978, 1979, and 1982.  A member of Physicians for Social Responsibility and the International Physicians for the Prevention of Nuclear War, Dr. Abraham was an author of the constitution of those organizations, and in 1985 shared in the awarding of the Nobel Peace Prize at Oslo. In 2007 he was elected Distinguished Life Fellow of the American Psychiatric Association. In 2014 he was awarded the honorary degree of Doctor of Humane Letters from Muhlenberg College. In 2017 he was recognized by the Distinguished Alumni Award of Johns Hopkins University School of Medicine.