Footage broadcast on CNN-Turk news channel showed protesters, some of whom had covered their faces with Palestinian-style chequered kaffiyehs, hurling incendiary devices at shops and in the streets in the Alibeykoy district in the city's European side and in the Sisli district.
A bus was set on fire in the Gazi neighbourhood while demonstrators pelted a police station with stones in the downtown Beyoglu, CNN-Turk said.
Riot police fired shots into the air to disperse about 150 protesters who had blocked a highway in Kadikoy district in the city's Asian side across the Bosphorus Strait, the Anatolia news agency said.
Thirteen demonstrators were detained in the incidents which erupted when the activists were prevented from going to the nearby town of Gemlik for a protest rally organised by a non-governmental organisation of prisoners' relatives against the prison conditions of Ocalan, Anatolia added.
Kurds want better prison
conditions for leader Ocalan
Local authorities had already banned the demonstration on the grounds that it was masterminded by Ocalan's outlawed Kurdistan Workers Party (PKK) which has waged a bloody campaign against Ankara since 1984.
Police and paramilitary gendarmerie troops, reinforced by forces from neighbouring towns, have set up checkpoints at all entrances to Gemlik and have stopped about 60 buses bringing in activists from around the country, several kilometres away from the town.
Ocalan has been in solitary confinement on a prison island in northwestern Turkey since being sentenced to death in 1999 for treason. His sentence was later commuted to life imprisonment.
Kurdish activists and the PKK have urged Ankara to move Ocalan to an ordinary jail on the grounds that solitary confinement is inhumane and conditions on the island are affecting his health.
Improving Ocalan's prison conditions was one of the demands made by the PKK's political wing, KONGRA-GEL, when it announced a one-month unilateral ceasefire to give Ankara time to improve Kurdish freedoms.
The truce has been brushed aside by the Turkish army.
Nearly 37,000 people have been killed since 1984 when the separatists first took up arms for self-rule in mainly Kurdish southeast Turkey.