The masks are back.

On Monday, major retailers and restaurant chains such as Home Depot Inc. and McDonald’s Corp., said they would require workers to wear masks in many of their stores, restaurants and offices regardless of vaccination status.

Some municipalities and local officials also said Monday they would start to impose new indoor mask mandates on residents in response to new federal health guidelines and rising U.S. Covid-19 cases.

The moves are the clearest signs yet that the coronavirus pandemic continues to be a challenge for U.S. business, and that employers are contending with ramifications of the fast-spreading Delta variant for employees and customers alike.

Last week, Walmart Inc. and Walt Disney Co. said they would mandate vaccines for some of their workers. Other firms delayed office reopening and some that are back open, such as Citigroup Inc., said they would require staff to wear masks inside offices regardless of their vaccination status.

Home Depot said its new mask policy for staff applies nationally.

Home Depot said its new mask policy for staff applies nationally.

Photo: Al Diaz/Associated Press

The shift followed the Centers for Disease Control and Prevention recommendation last week that vaccinated people resume wearing masks in some indoor spaces, reversing its earlier guidance. On Friday, the CDC said vaccinated people may spread the Delta variant.

The latest statistics from the CDC show a 64.1% increase in Covid-19 cases over the week ended July 30 compared with the previous week, or an average of 66,606 cases a day. The CDC reported a current seven-day average of 6,071 new admissions of hospital patients with Covid-19, a 44% increase over the average for the week of July 16-22. CDC Director Rochelle Walensky previously has said that more than 97% of Covid-19 patients entering the hospital nationwide were unvaccinated.

It remains to be seen how much the recent jump in U.S. cases and heightened concerns affect consumer sentiment, promoting people to rethink travel plans or their willingness to dine out or shop in stores, which could dent rebounding sales for many businesses.

Local officials in California, Louisiana and other states said they would begin to require people to wear masks indoors starting this week, while New York City officials are recommending that residents wear face coverings indoors.

Many businesses are changing their policies just as they were preparing to return to normal operations after the Labor Day weekend and the restart of the school year. Most retail and restaurant chains are requiring employees to wear masks, while suggesting customers do the same but not requiring them to do so.

Retailers and restaurants have benefited from a surge of in-person dining and shopping in recent months.

While Covid-19 vaccinations are highly effective at preventing hospitalizations or death from the virus, they’re not foolproof in preventing infection. This poses problems for events like the Olympics and raises broader questions about immunity in the long term. Photo: David Crigger/Bristol Herald Courier/Associated Press The Wall Street Journal Interactive Edition

Home Depot said Monday it would require all workers nationally to wear masks regardless of vaccination status, while Target and McDonald’s said they would only require mask wearing for all employees in counties deemed at high risk for Covid-19 transmission by the CDC.

McDonald’s updated policy applies to both company- and franchisee-owned restaurants and came in response to the federal government’s new mask recommendations, the burger chain said.

Starbucks Corp. said Monday that it will require all workers in its roughly 8,900 company-operated U.S. cafes to wear masks regardless of vaccination status or location, starting Thursday. Starbucks said it was recommending facial coverings for all patrons, and requiring them where local officials now mandate masks.

In a message to employees explaining the different rules, Starbucks said customers are inside stores for shorter periods, employees spend more time with each other in close proximity and “we want to reduce the risk of potential exposure by removing any need for you to enforce or de-escalate a customer who is refusing to wear a mask.”

Restaurant companies have largely reported rebounding sales in their most recent quarter, and the Delta surge now threatens to slow some of that momentum, consumer surveys show. Diners who characterize themselves as the most anxious about the coronavirus were the last to return to dining out, helping to fuel sales this spring and summer, according to Lisa W. Miller & Associates, a consumer research firm. The most nervous Americans are very concerned about the Delta variant and pulling back on their activities, surveys by the firm have found.

While most retail and restaurant chains are encouraging customers to wear masks, putting up new reminders and giving out masks, they are stopping short of imposing mandates on shoppers.

Like Walmart, Home Depot and Target said Monday they would encourage, but not require, all shoppers to wear masks in high-risk areas. Target said workers and shoppers outside high-risk areas would continue to be able to drop masks if vaccinated.

Last week Walt Disney said it would require customers to wear masks indoors at its U.S. theme parks. Apple Inc. has also required shoppers and employees to wear masks in about half of its stores.

Walmart is also mandating some corporate workers and managers to be vaccinated, but not the people who work in its stores and warehouses. Target offers vaccine appointments at most in-store CVS pharmacies and provides paid time off for vaccine appointments.

Other businesses continue to announce similar requirements. The developer of Hudson Yards in New York City, Related Cos., will require its staff to have received at least a first shot of the Covid-19 vaccine by Aug. 31, the real-estate firm said in an email to employees on Monday.

In April, the company told employees that being vaccinated would be a requirement once there was enough supply. Its roughly 1,000 corporate staffers were required to be in compliance with the vaccine mandate on June 1 and Monday’s move extends the mandate to its broader staff.

Those with medical or religious exemptions will be required to undergo regular testing, the memo reads. A spokesman for the company said Related has roughly 4,000 employees.

Facebook said Monday it will require any employee working at its U.S. offices to wear a mask, regardless of vaccination status. The social-networking giant last week said that employees working at its U.S. office would need to be vaccinated.

The new masking policy takes effect Aug. 3 and will remain in place until further notice, the company said. Many of Facebook’s U.S. employees remain at home. The company has previously said it plans to reopen its U.S. offices more broadly this fall.

—Chip Cutter and Robert Barba contributed to this article.

Write to Sarah Nassauer at sarah.nassauer@wsj.com and Heather Haddon at heather.haddon@wsj.com

Corrections & Amplifications
An earlier version of this article misidentified Home Depot Inc.’s corporate designation as Home Depot Corp. (Corrected on Aug. 2)