Unrest was also reported in the working-class neighbourhoods of Djebel Lahmer and Zahrouni on the outskirts of Tunis, the central cities of Gafsa and Kasserine, and the northern town of Jedaida.
In the central town of Sidi Bouzid, the cradle of the protests that sparked the 2011 uprisings, youths blocked roads and hurled stones, causing the police to retaliate with tear gas, an AFP reporter said.
A representative of Tunisia's Jewish community said two Molotov cocktails were thrown at the entrance to two Talmudic schools on the Mediterranean island of Djerba, but their interiors were not damaged.
The recent unrest started with peaceful protests against the austerity measures last week, but escalated into clashes with police in the night of Monday to Tuesday.
Activists have called for a massive demonstration on Friday against the austerity measures, which are expected to increase the cost of living.
They have called for the revision of the legislation behind the VAT and social contribution hikes, as well as better welfare for struggling families.
"There are acts of looting and robbery but also a political message from a section of the population that has nothing to lose and feels ignored" seven years after a revolution demanding work and dignity, said political scientist Selim Kharrat.
He said that many public buildings have been targeted while the government has "taken a pretty strong stance against the protesters".
The powerful UGTT trade union said young unemployed Tunisians had legitimate demands but condemned the "violence and looting", calling for peaceful protests.
Tunisia's economy has struggled since the 2011 revolution, which was fuelled by unemployment and graft.
Protests are common in the North African state in the month of January, when Tunisians mark the anniversary of the revolt that unseated dictator Zine El Abidine Ben Ali.
January 2016 saw the biggest wave of public discontent since the uprising as the death of an unemployed protester in Kasserine sparked days of unrest.
In December, unemployed protesters and activists marched through the streets of Sidi Bouzid, angry over the lack of jobs and opportunities that continue to plague residents.
The revolution in Tunisia began in the town in December 2010 after street vendor Mohamed Bouazizi set himself on fire and later died in a protest over unemployment and police harassment that spiralled into Ben Ali's overthrow.