Elvan went into coma after being hit by a tear gas canister during an anti-government demonstration in June.
The protesters, led by Taksim Solidarity Platform, had just finished reading a statement to call on those responsible for Elvan’s injury to be brought to justice when the clashes erupted.
According to Turkey’s Dogan news agency, some 18 protesters were arrested.
A similar demonstration was held in September, with protesters calling for justice in Elvan’s case.
Earlier this year, Turkey witnessed weeks of mass demonstrations after Turkish police broke up a sit-in held at Istanbul's Taksim Square to protest against a proposal to demolish Gezi Park on May 31.
The violence turned into nationwide demonstrations against the ruling Justice and Development Party and Prime Minister Recep Tayyip Erdogan, with police using water cannons, tear gas and rubber bullets against the demonstrators.
Several people were killed and many more injured and detained as police forcefully cracked down on the daily protests.
Erdogan faced international condemnation for his handling of the crisis and the Turkish police were strongly criticized for using excessive force against peaceful protests.
Erdogan had described the protesters as vandals, looters or terrorists, and claimed the demonstrations were part of a plot to topple his government.