But critics said the loose covering known as the niqab did not offer sufficient protection and it was another attempt to impose conservative dress codes on women in the world's biggest Muslim-majority nation.
Mohammad Suhaili Fadhil Thohir, the head of Central Lombok regency, next to the holiday island of Bali, said he made the order after government employees complained about wearing face masks during office calisthenics held outside every Friday -- Islam's holy day.
But Thohir denied any religious motivation for requiring the face veil, which is not worn by most women in Indonesia but is common in some Gulf nations.
"It is purely for Covid-19 prevention. This is not based on radical teachings or fanaticism," Thohir said, adding that there were no sanctions for ignoring his rule.
"To make sure civil servants cover their nose and mouth during the weekly exercise we asked them to wear veils."
The policy was announced last month. Male civil servants have to wear medical masks during the group exercises.
While the rule may only be mandatory on Fridays, many female employees wear veils in the local government office on other days, according to an AFP reporter.
About 90 percent of the nearly 4,000 women working for Central Lombok's government are Muslim.
Civil servant Yayuh, who like many Indonesians goes by one name, said she expected Central Lombok's policy would become mandatory during all work hours.
"But I don't mind as it's a way to learn about wearing appropriate clothes taught in Islam," she added.
The policy has raised eyebrows among rights groups.
"A mask needs to meet certain standards to prevent" infection, said Andy Yentriyani, a commissioner at the National Commission on Violence Against Women.
"The policy should be reviewed because it could threaten women's health rights."
Central Lombok has got off relatively lightly with the virus, with 117 confirmed cases and four deaths. Nationwide infections have officially topped 70,000.
Indonesia's long-held reputation for being relatively liberal has taken a hit in recent years as Muslim hardliners gain influence.
This week police in conservative Aceh province -- where wearing the hijab, which covers a woman's hair and neck, outside is mandatory -- censured a group of female cyclists over what authorities deemed inappropriate clothing: tight, long-sleeved pink tops and dark trousers.
Human Rights Watch researcher Andreas Harsono said the veil order was "obviously an extension" of a mandatory hijab regulation for Muslim girls in almost 300,000 public schools across the sprawling archipelago.
"Everyone should wear masks to protect themselves from the coronavirus, including civil servants, but a veil is not a mask," he said. - AFP