The rally, which gathered some 500 people, had begun peacefully at Istiklal Street in the centre of the European side of the city on Tuesday.
Police intervened as demonstrators attempted to form a human chain and shouted slogans against the government of President Recep Tayyip Erdogan and its offensive against Kurdish militants.
Jets from a water cannon were fired down the middle of the street -- a busy shopping area -- and police used tear gas as demonstrators ran for cover.
Among those detained was Yasin Akgul, a Turkish freelance photographer who works as a stringer for Agence France-Presse (AFP).
He was pinned to the ground by several police as he tried to take pictures of the arrests.
Akgul was taken to a waiting police van before being released after colleagues remonstrated that he was a media photographer.
Akgul was given hospital treatment for an arm injury but was later allowed to go home.
Reports said a cameraman from the state-run Anatolia news agency was also injured.
Anatolia reported that a total of 14 people had been arrested.
Turkish cities are tense as the government presses a controversial campaign against Kurdistan Workers Party (PKK) militants, with security forces clamping down on any signs of large scale protest.