The three-hour skirmish was initiated by activists belonging to the Committee to Resist Anti-Quran Laws, a coalition of Islamic parties.
The protests were against a women's development policy adopted in March by the government, advocating equal property rights for women.
Dozens were injured in similar clashes on Thursday.
Muslim clerics and parties have warned of nationwide demonstrations, saying they will not tolerate any laws that contradict Sharia, or the Islamic legal code.
'Playing with fire'
"I can't tolerate it ... anything that goes against Islam," Mohammad Abdur Rahman, a protester, said. "The government is playing with fire."
Rights activists say there is nothing in the policy that undermines Islamic law.
"It's unacceptable that some groups are trying to make it a point," Ayesha Khanam, a leading women's rights activist, said.
"The policy is not a law, just a guideline that conforms to various women's rights charters," she said.
"It has no clash with Islam."
Soon after the new policy was announced, the government backed down, explaining it had not been passed into law. No legislation would be passed "that goes against the Quran and the traditions of Prophet Muhammad," the government said.
Bangladesh, whose population is 90 per cent Muslim has a secular legal system but in matters related to inheritance and marriage Muslims follow Sharia law.
This generally stipulates that a girl inherits half of what her brother gets. Women's groups have long protested against the disparity and demanded equal rights.