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Employers could impose hefty penalties on employees who decline to participate in genetic testing as part of workplace wellness programs if a bill approved by a U.S. House committee this week becomes law.

In general, employers don't have that power under existing federal laws, which protect genetic privacy and nondiscrimination. But a bill passed Wednesday by the House Committee on Education and the Workforce would allow employers to get around those obstacles if the information is collected as part of a workplace wellness program.

Such programs — which offer workers a variety of carrots and sticks to monitor and improve their health, such as lowering cholesterol — have become increasingly popular with companies. Some offer discounts on health insurance to employees who complete health-risk assessments. Others might charge people more for smoking. Under the Affordable Care Act, employers are allowed to discount health insurance premiums by up to 30 percent — and in some cases 50 percent — for employees who voluntarily participate in a wellness program where they're required to meet certain health targets.

The bill is under review by other House committees and still must be considered by the Senate. But it has already faced strong criticism from a broad array of groups, as well as House Democrats. In a letter sent to the committee earlier this week, nearly 70 organizations— representing consumer, health and medical advocacy groups, including the American Academy of Pediatrics, AARP, March of Dimes and the National Women's Law Center — said the legislation, if enacted, would undermine basic privacy provisions of the Americans With Disabilities Act and the 2008 Genetic Information Nondiscrimination Act (GINA).

Congress passed GINA to prohibit discrimination by health insurers and employers based on the information that people carry in their genes. There is an exception that allows for employees to provide that information as part of voluntary wellness programs. But the law states that employee participation must be entirely voluntary, with no incentives for providing the data or penalties for not providing it.

But the House legislation would allow employers to impose penalties of up to 30 percent of the total cost of the employee's health insurance on those who choose to keep such information private.

“It's a terrible Hobson's choice between affordable health insurance and protecting one's genetic privacy,” said Derek Scholes, director of science policy at the American Society of Human Genetics, which represents human genetics specialists. The organization sent a letter to the committee opposing the bill.

The average annual premium for employer-sponsored family health coverage in 2016 was $18,142, according to the Kaiser Family Foundation. Under the plan proposed in the bill, a wellness program could charge employees an extra $5,443 in annual premiums if they choose not to share their genetic and health information.

The bill, Preserving Employee Wellness Programs Act, HR 1313, was introduced by Rep. Virginia Foxx, (R-N.C.), who chairs the Committee on Education and the Workforce. A committee statement said the bill provides employers “the legal certainty they need to offer employee wellness plans, helping to promote a healthy workforce and lower health care costs.” It passed on a party-line vote, with all 22 Republicans supporting it and all 17 Democrats opposed.

The bill’s supporters in the business community have argued that competing regulations in federal laws make it too difficult for companies to offer these wellness programs. In congressional testimony this month, the American Benefits Council, which represents major employers, said the burdensome rules jeopardize wellness programs that improve employee health, can increase productivity and reduce health care spending.

A House committee spokeswoman told CNBC that those opposed to the bill “are spreading false information in a desperate attempt to deny employees the choice to participate in a voluntary program that can reduce health insurance costs and encourage healthy lifestyle choices.”

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