American frackers, already struggling to hire enough workers, are concerned that the coming U.S. vaccine mandate will worsen the situation at a time of rising oil and gas prices.

Many of the truckers, rig hands and roustabouts who used to work in Texas and other oil patch regions found other jobs after crude prices crashed last year during the onset of the pandemic.

Oil-field service companies, which employ most of the ground-level workers who drill and finish wells, say many remaining employees are skeptical about Covid-19 vaccination, and some have warned they would quit before getting shots.

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The proposed mandate doesn’t require companies to terminate employees who don’t comply, but those workers would be subject to frequent testing. Some companies are concerned that such testing would frustrate unvaccinated employees and motivate them to leave their jobs.

Ann Fox, chief executive of Nine Energy Service Inc., an oil-field service company active across the U.S., said she is worried that it could lose a portion of its workforce of 818, most of which are field-level employees. The company is already dealing with rapid turnover—roughly two out of every three recent new hires tend to leave after a short period, she said.

“It places all of us in leadership positions in tremendously complex situations,” Ms. Fox said, estimating that less than 15% of the company’s field-level workers are vaccinated. Nationwide, 65% of eligible people are fully vaccinated, according to the Centers for Disease Control and Prevention.

Ms. Fox said many in the industry were also concerned about requirements for weekly testing for unvaccinated workers, saying it could be burdensome to administer and manage, with so many small crews working in rural areas.

For now, companies are awaiting guidance on how President Biden’s plan to require Covid-19 vaccines or weekly testing for all employers with 100 or more workers will be implemented. Mr. Biden directed the Occupational Safety and Health Administration, or OSHA, to impose such a mandate earlier this month.

But many oil-field service companies are already anticipating problems, based on vaccination rates in the areas where they operate and feedback from their workers.

In Midland County, Texas, the heart of the Permian basin, the most active U.S. oil field, about 46% of eligible people have been fully vaccinated, according to the Texas Department of State Health Services, compared with the state’s overall rate of 61.5%. The region is seeing a plateau in Covid-19 hospitalizations after a monthslong rise that pushed hospitals to near their limits, local health officials said.

Clint Concord, senior operations manager at Byrd Oilfield Services LLC in Odessa, Texas, said many in the oil patch are skeptical of the safety and efficacy of Covid-19 vaccines—including himself. He said he would need to weigh his own options, but that frequent testing for unvaccinated workers might lead him to quit.

“It’s our constitutional right not to put something in our body if we don’t want to,” Mr. Concord said. “They haven’t proven to me this is 100% stable.”

The Food and Drug Administration has said that the vaccines it has authorized in the U.S. have been demonstrated to be safe and effective.