Turkish broadcaster NTV reported the deputy mayor of the city’s Sisli district is in a critical condition.
They say an unknown assailant entered the office of Cemil Candas and several shots were heard.
It is unknown if the shooting is connected to the attempted coup.
Meanwhile, dramatic footage has emerged of an attack on the Turkish intelligence agency headquarters during last Friday’s failed coup.
Video provided by the country’s National Intelligence Agency shows gunfire – apparently from a helicopter – strafing the entrance to its HQ in Ankara.
Cars screech to a halt to avoid the bullets and security staff are seen on the CCTV footage firing handguns and automatic weapons into the sky in retaliation.
The footage emerged as the president’s office said F-16 fighter jets will continue to patrol airspace over Istanbul and Ankara following the failed coup attempt.
Recep Tayyip Erdogan has also given his country’s air force orders to shoot down any military helicopters taking off from Istanbul, the source added.
Turkey has reportedly suspended almost 8,000 police officers following Friday’s failed coup.
A total of 8,777 public officials, also including 30 governors and more than 50 high-ranking civil servants have been removed from their posts, while 103 generals and admirals are among those arrested, according to Turkish media.
The purge of state structures and presence of F-16 jets suggests authorities fear the threat against Mr Erodgan is not over, even amid a crackdown that has seen more than 7,500 people arrested.