The suspect, who was detained after a chase by a police officer and a former police officer, allegedly walked into the office and shot the victims, Zion Precinct Commander Brig. Gen. Amnon Alkalai said.
The victims, who names weren't release, were a man, 56, and his 26-year-old daughter, the Tel Aviv newspaper Maariv reported.
"Both suffered a number of gunshot wounds in the upper body. They were unconscious, without a pulse ... we were forced to pronounce them dead," paramedic Yisrael Cohen told Maariv.
"We still don't know how the suspect is connected to the victims," Alkalai said.
Jerusalem Mayor Nir Barkat, at the scene Tuesday, said the motive for the shooting was unclear, the Israeli news website Haaretz reported.