The incident took place at the Benjamin Franklin Hospital in the Steglitz district of Berlin at around midday.
By shorty after 2.30 pm Berlin police announced via Twitter that the doctor had died.
The doctor was the head doctor in the jaw surgery department and a father of two, reports Tagesspiegel.
Police confirmed later on Tuesday that the murderer was a 72-year-old German man who had been treated the previous day in the hospital.
Police earlier tweeted that they have no indication that there was a terrorist motive to the shooting.
The injured doctor had been taken into intensive care after the shooting, the background to which is still unclear.
Der Arzt wurde nach ersten Erkenntnissen lebensgefährlich verletzt & befindet sich in intensivmedizinischer Behandlung. Weitere Infos folgen— Polizei Berlin (@polizeiberlin) July 26, 2016
According to the Tweet, after attacking the doctor, the perpetrator shot himself.
Germany has been shaken by a series of violent incident over the past eight days, including a shooting spree in Munich that left ten people dead.
There is as yet no know motive for Tuesday's shooting. However Tagesspiegel reports that the gunman was a former patient of the doctor.
Eyewitnesses also told Tagesspiegel that police special forces were in operation at the hospital and had entered in large numbers.
A later Tweet from police said there was "no danger" at the hospital and that the situation was under control. They also stressed the importance of avoiding spreading rumours.
At roughly 2.30 pm police tweeted that they had no indication that any further people had been injured during the shooting, or that there were any other gunmen.
The Benjamin Franklin Hospital is one of four campuses which belong to the Charite Hospital in Berlin. According to Bild it has around 900 beds.