More Americans are being tested for Covid-19—and waiting longer for results—as virus cases surge and places from offices to concert venues require people to show proof they aren’t infected.

The nation’s Covid-19 testing infrastructure, from health systems and pharmacies to diagnostic labs, are racing to keep up as the highly contagious Delta variant spreads in many parts of the country. Workplace testing requirements and revised federal guidelines recommending that vaccinated people exposed to Covid-19 get tested could be adding to the demand.

Delayed results can hamper efforts to contain the spread of the virus and interfere with attendance at work, school or other activities that require proof of a negative test. Testing shortages and logjams complicated efforts to contain Covid-19 surges last year.

A Covid-19 swab test is collected at another Houston drive-through site.

Photo: Mark Felix/Bloomberg News

CVS Health Corp. said Wednesday that demand for testing at its locations is now well above daily averages for this year. Meanwhile, at-home tests are among the company’s top-selling products in stores.

“People are obviously feeling symptoms and getting tested in greater numbers,” CVS Chief Executive Karen Lynch said in an interview. She said CVS has ample capacity to handle demand.

The lab company Quest Diagnostics Inc., which had testing backlogs last summer, said this week that it is evaluating alternatives to add capacity as demand increases. Quest said it is able to report most Covid-19 test results within a day.

On Wednesday morning, a line of 14 people waited outside a CityMD clinic on New York City’s Upper West Side. An employee at the front door predicted a 40-minute wait, and a sign taped to the glass warned of a three- to five-day turnaround on polymerase chain reaction test results.

Jude Hunt, 81 years old, said she was waiting in line for her second PCR test this week after her vaccinated housekeeper tested positive. She said she previously contracted Covid-19 and received the vaccine, but added, “After the last two years, I’m not taking any chances.”

David Gallego, a medical tech at a LabQ mobile-testing site around the corner from the CityMD, said he has seen the number of people stopping by for Covid-19 tests double in the past couple of weeks, to about 100 people a day.

“Either they’re travelers, people who have symptoms or people who are scared because they felt like they’ve been exposed,” he said.

A spokeswoman for Summit Health, parent of CityMD, said the company has seen a recent surge in demand for tests and is working to address it.

Laboratories in the U.S. processed a seven-day average of 713,000 daily tests for the virus’s genetic material as of Aug. 2, according to data from the Department of Health and Human Services. That is an increase from about half a million in early July but remains below peaks of more than two million daily tests during the fall and winter surges.

More than 9% of tests are coming back positive, up from the lowest recorded rate of around 2% in June.

As the Delta variant sweeps the globe, scientists are learning more about why new versions of the coronavirus spread faster, and what this could mean for vaccine efforts. The spike protein, which gives the virus its unmistakable shape, may hold the key. Illustration: Nick Collingwood/WSJ The Wall Street Journal Interactive Edition

Earlier this year, the rollout of Covid-19 vaccines and declining U.S. cases caused testing demand to plummet. Many testing sites closed or were converted into vaccination clinics.

“Several months ago, you could in Massachusetts go to many sites and get a free test really quickly, walk in,” Ezekiel Emanuel, co-director of the Healthcare Transformation Institute at the University of Pennsylvania, said at a recent media briefing. “They closed all those places, and it’s really now hard to actually get a test and especially a test on a weekend.”

In another change, antigen tests, which hunt for the virus’s proteins and can provide results at home in 15 minutes, are now available over the counter and online across the country. That provides test takers with another option but also leaves a hole in Covid-19 data, because there is often not a clear or reliable way to get those results to public-health officials.

Tips for Getting a Covid-19 Test

Mary Hayden, an infectious-disease specialist in Chicago, expects testing delays to be temporary: Testing sites and infrastructure are in place, but need to staff back up, she said. For now, she recommends checking online to see whether local testing centers provide estimated wait times.

Dr. Hayden also suggests looking into home testing. “Big, national commercial labs have tremendous capacity and usually don’t ramp up and down like a hospital lab,” said Dr. Hayden.

Take-home tests from a local pharmacy are another option, said Dr. Gigi Gronvall, a senior scholar at Johns Hopkins Center for Health Security. “If you’re symptomatic, those rapid tests are very accurate, and they’re not complicated to use,” she said. “But if you are struggling with the directions, there are YouTube videos.”

Last week the Centers for Disease Control and Prevention revised testing guidance as well as masking guidance. The agency recommended that fully vaccinated people be tested three to five days following a Covid-19 exposure and wear masks in public indoor settings for two weeks or until they receive a negative test result. Previously the CDC had said fully vaccinated people didn’t need to be tested after an exposure if they didn’t have any symptoms.

In Lansing, Mich., which had a severe outbreak this spring, local health officials decided to keep open a mass testing and vaccination site at a closed Sears department store.

Five of seven bays repurposed for drive-up Covid-19 tests are in use after weeks of using just two or three, said Alan Vierling of Lansing’s Sparrow Health System. His main concern if demand surges: finding enough people to staff the site in a tight labor market.

“We felt like it was coming back and that we should keep our infrastructure in place,” he said of the virus. “The next one is going to be Delta, then there will likely be another one and then another one.”

Write to Sharon Terlep at sharon.terlep@wsj.com and Brianna Abbott at brianna.abbott@wsj.com