"Mirza Fakhrul Islam Alamgir has been picked up by officers of the law enforcing agency," the Bangladesh Nationalist Party said in a statement.
«He has been detained by police officers,» Shamaruh Mirza, Alamgir's daughter who lives in Australia, told AFP.
Dhaka Metropolitan Police spokesman Faruk Hossain said he was not aware of his arrest.
Alamgir, 75, the BNP's secretary-general, has been leading the party since BNP chairwoman and two times former premier Khaleda Zia was arrested and jailed, and her son went into exile in Britain.
Zia has been living under effective house arrest since her release from a 17-year prison sentence in 2020.
The protests on Saturday by the BNP and the largest Islamist party, Jamaat-e-Islami, were the biggest so far this year, AFP journalists on site said, and marked a new phase in their protests with a general election due before the end of January.
More than 100,000 supporters of two major Bangladesh opposition parties rallied to demand Prime Minister Sheikh Hasina step down to allow a free and fair vote under a neutral government.
Hasina — daughter of the country's founding leader — has been in power for 15 years and has overseen rapid economic growth with Bangladesh overtaking neighbouring India in GDP per capita, but inflation has risen and her government is accused of corruption and human rights abuses.
Both BNP and Jamaat-e-Islami called for a nationwide strike on Sunday to protest the violence.
Security on Sunday was tight in the capital with thousands of police and paramilitary Border Guard Bangladesh patrolling the streets.