The authorities announced 44 people were detained nationwide overnight as several official buildings were damaged and 11 policemen wounded by stones and Molotov cocktails.
Officials said an autopsy would help determine how a 43-year-old man died in the town of Tebourba, west of Tunis. The police insisted they did not kill him, and said he suffered from "respiratory problems".
On Tuesday small peaceful rallies were held in the centre of the capital Tunis and at least one other town calling for the end of austerity measures that are expected to increase the cost of living.
Tunisia has seen several days of protests after activists and politicians denounced hikes in value-added tax and social contributions introduced at the start of the year as a tough new budget was implemented.
Prime Minister Youssef Chahed decried the unrest, telling local radio that "we didn't see protests, but instead people breaking things, stealing and attacking Tunisians".
"The government is ready to listen, but every person wanting to demonstrate must do so peacefully," he said.
Blazing tyres, stones thrown
Protests are common in the North African state in the month of January, when Tunisians mark the anniversary of the 2011 revolt that unseated dictator Zine El Abidine Ben Ali.
The country has been hailed for its relatively smooth democratic transition but seven years after the revolution tensions over economic grievances are high.
Overnight AFP reporters saw police fire tear gas at youths in the impoverished city of Kasserine who torched tyres and threw stones.
Protesters blocked roads in the town of Sidi Bouzid, the cradle of the uprising against Ben Ali.
An interior ministry spokesman said at least 44 people had been arrested, including 16 in Kasserine and 18 in working-class areas near Tunis.
A car pound in Kasserine was ransacked, Khalifa Chibani said, and buildings of the security forces damaged in the southern town of Hamma.
The unrest "had nothing to do with democracy or social demands", he told the Shems FM radio station.
National Security agency spokesman Walid Ben Hkima denounced "acts of violence and ransacking" and said four police vehicles were also damaged.
Finance Minister Ridha Chalghoum told AFP that the government intended to stick with its tax rises, but insisted the VAT hike did not cover "basic necessities".
"Among the achievements of democracy is the opportunity to demonstrate, but we also have an obligation to work for a healthy Tunisian economy," he said.
Tunisia's economy has struggled since the revolution, with growth remaining slow.
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.
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