When the protesters tried to march into the main business district, police fired tear gas and used batons to disperse them, a police officer said on condition of anonymity because he was not authorized to speak to reporters. Protesters hurled rocks at the troops, he said.
There were no immediate reports of injuries.
An alliance of Kashmiri religious groups called the strike in response to the anti-Islam film.
The shutdown was supported by the bar association, trade unions and separatist groups in the volatile region, where strikes are a common tactic to protest against rule.
In Indonesia, about 200 people from various Islamic groups torched an American flag and tires outside the US Consulate in the third largest city of Medan. Some unfurled banners saying, "Go to hell America," while others trampled on dozens of paper flags.
Also Tuesday, about 100 Muslim students in Makassar, a city in central Indonesia, called for the death penalty against the filmmaker, Nakoula Basseley Nakoula.
The government in Bangladesh blocked YouTube on Monday to prevent people from seeing the video. Mir Mohammaed Morshed, a spokesman for the state-run Bangladesh Telecommunications Company Ltd, said the decision will remain effective until further notice.
Google has blocked access to the video in Libya and Egypt following violence there, and in Indonesia and India because it says the video broke laws in those countries.
