The protesters burned several vehicles, including a police van, witnesses said.
Dozens of protesters were arrested at the demonstration and inside the nearby National Press Club, where participants took refuge, a Dhaka Metropolitan Police official said on condition of anonymity in line with police policy. Police and witnesses said scores of people were injured.
The clash erupted when authorities attempted to halt the demonstration, police said. Authorities have banned all protests near the city's main Baitul Mokarram mosque since Friday, when more than 2,000 people marched and burned an effigy of President Barack Obama.
The protesters announced a nationwide general strike on Sunday to protest the police action.
In Lebanon, the Shiite militant group Hezbollah organized another protest rally Saturday in the southern border town of Bint Jbeil, the latest in a series of demonstrations.
In Pakistan, protests continued Saturday, with more than 1,500 people, including women and children, rallying in the capital. The crowd was peaceful but angry over the release of the video called "Innocence of Muslims," which portrays Prophet Muhammad as a fraud, a womanizer and a child molester.
The protesters from the Minhaj-ul-Quran religious group marched through Islamabad's streets and then gathered near Parliament, chanting slogans against the filmmaker and demanding stern punishment for him.
Turkish Prime Minister Recep Tayyip Erdogan criticized the recent violent protests, but said Western nations need to prevent insults to Islam.
"No one claims freedom of expression when they restrict racism. The same restrictions that are imposed on racism must be displayed against Islamophobia," Erdogan said Saturday. "Islamophobia is as dangerous as racism and is something that must not be tolerated."
Thousands of people also protested Saturday in Nigeria's largest city, Kano. The crowd marched from a mosque to the palace of the Emir of Kano, the region's top spiritual leader for Muslims.
About 200 students in Srinagar, the main city in Indian-controlled Kashmir, chanted "Down with America" and "Long live Islam" in a peaceful protest. Some carried a placard that read, "There is no God but Allah and Muhammad is his messenger."