A Jeep Renegade rolls down an assembly line at Fiat Chrysler's Melfi assembly plant in Italy in 2015.

Fiat Chrysler said Wednesday that it will "intensify measures" against the spread of the coronavirus in Italy, including temporarily closing plants there, where the government has implemented a national quarantine.

The shutdowns are staggered through this week. They include three days at three plants that produce Fiat and Alfa Romeo vehicles and two days at another plant that assembles small Jeep and Fiat crossovers. Some of the Jeep, Fiat and Alfa Romeo products are imported to the U.S.

The new measures come as Italy has 10,149 confirmed cases of the COVID-19 virus, according to Johns Hopkins University and Italy's civil protection agency, and 631 deaths from the virus, up 168 from Monday.

Other announced measures Wednesday by Fiat Chrysler include additional "intensive sanitation of work and rest areas," a work from home program for office-based employees and the slowing down of production lines to enable greater spacing of employees at their workstations.

"Fiat Chrysler Automobiles is implementing new measures across its facilities in Italy to support the nationwide campaign addressing the COVID-19 crisis," the Italian-American automaker said in a release.

Public gatherings in Italy are banned – ranging from weddings to funerals, sports events and religious services – and Italians are encouraged to stay home and "limit social contact as much as possible." Travel is only allowed for urgent work situations and emergencies or health reasons.

There are signs that even stricter measures, including a countrywide shutdown, could be imposed.

North American production for Fiat Chrysler has not been impacted by the coronavirus, according to a company spokesman.

— CNBC's Holly Ellyatt contributed to this report.