The incident occurred shortly before noon at Brigham and Women's Hospital on Tuesday. The shooter killed himself after the incident.
The hospital said Michael Davidson, director of endovascular cardiac surgery, died late Tuesday from gunshot wounds.
"Dr. Davidson was a wonderful and inspiring cardiac surgeon who devoted his career to saving lives and improving the quality of life of every patient he cared for," it said in a statement.
Police named the shooter as Stephen Pasceri, 55. His mother had been a patient of Davidson and Boston police said the doctor had been deliberately targeted.