Police fired tear gas to disperse hundreds of protesters in the centre of Tataouine city, an AFP correspondent said.
Defence Ministry spokesman Mohamed Zekr said the army was deployed outside state establishments.
Demonstrators at a protest camp in the region have been demanding authorities make good on a 2017 promise to provide jobs in the gas and oil sector to thousands of unemployed.
For weeks they have blocked roads around the remote El Kamour pumping station to prevent tanker trucks from entering the facility, but the protest had been largely peaceful.
On Sunday, protesters in Tataouine city burned tyres and pelted security forces with stones to demand jobs and the release of activist Tarek Haddad, who was arrested the previous day, as security forces responded with tear gas.
Haddad is a key figure in the protest movement.
The governor of Tataouine, Adel Werghi, said Haddad was "wanted" by the authorities, without providing further details.
The interior ministry said 10 people were arrested Sunday after a group of protesters tried to attack police stations with Molotov cocktails.
Denouncing an "excessive and unjustified" use of force against protesters, the powerful Tunisian trade union confederation UGTT had called for a general strike in Tataouine.
Shops were open on Monday but public services and state institutions remained closed in adherence to the strike, AFP correspondents said.
In 2017, protesters blockaded Tataouine's El Kamour pumping station for three months demanding jobs.
The sit-in ended after the employment minister signed a deal with representatives of the protesters, brokered by the UGTT, pledging to invest 80 million Tunisian dinars a year (almost $28 million) in Tataouine.
The UGTT branch in Tataouine said the promise was never kept.
The protests come as Tunisia, until now largely spared the worst of the novel coronavirus, faces tensions within its coalition government and the impact of restrictions imposed to combat the spread of the pandemic that have deepened inequalities.