Four people have died in the rare unrest, the interior minister said.
Ousmane Sonko appeared in court on Friday accused of disrupting public order. He also faces a rape allegation.
He denies the allegations and his supporters say the accusations are politically motivated.
On Friday Interior Minister Antoine Felix Abdoulaye Diome vowed to use "all the means necessary for a return to order".
Speaking on national TV, Mr Diome accused Mr Sonko of "issuing calls to violence".
UN Secretary-General Antonio Guterres has urged protesters and police to refrain from violence in the nation which is one of West Africa's most stable countries.
On Friday police fired tear gas at Mr Sonko's supporters, who set up makeshift barricades in the capital Dakar where the ground was covered in burnt debris and people chanted "Free Sonko".
Police blocked motorbikes and mopeds, which are popular among Mr Sonko's young supporters, from the city's streets. A supermarket in Dakar's suburbs was raided on Friday, according to AFP news agency.
"What we are living through in this country is incredible, it is shameful," one protester told Reuters news agency.
Demonstrators have gathered in the city's surrounding areas and in the southern city of Bignona, a stronghold of Mr Sonko.
Two private TV channels that covered the protests have been suspended for 72 hours by the government.
On Thursday Internet monitor NetBlocks said access to social media and messaging apps was restricted.
The United Nations' special envoy for West Africa Mohamed Ibn Chambas has appealed for calm.
Some of the protesters have targeted French-owned businesses such as supermarkets and petrol stations because they say that under President Macky Sall, France has extended its economic interests in its former colony.
Mr Sonko, 46, was accused of rape in February by a woman who worked in a beauty salon.
Following an investigation he was arrested on Wednesday and taken to court accompanied by a group of supporters.
Police said they then arrested him for disrupting public order when he refused to change his route to the court.
Mr Sonko says the allegations of rape are fabricated. He accuses President Sall of trying to remove potential opponents ahead of the 2024 election. Two other opposition leaders were excluded from the 2019 election after being convicted on charges which they say were politically motivated.
There are reports that Mr Sall may seek to change the constitution to allow him to run for a third term.
Mr Sonko is the president's only remaining serious challenger, BBC Afrique's Ndèye Khady Lo in Dakar says.
She explains that the opposition politician is particularly popular with young Senegalese for his promise of radical opposition to what he calls "the system".
In 2014 he founded his own political party, Pastef-Les Patriotes, and came third in the 2019 presidential election with 15% of the vote.
In a video recorded and shared on social media in 2018, Mr Sonko told activists: "There is enormous potential in this country. It is unacceptable to see suffering of our people.
"Our politicians are criminals. Those who have ruled Senegal from the beginning deserve to be shot."