The spouses of highly skilled foreign workers would no longer be able to work legally in the U.S. under a regulatory change proposed by the Trump administration on Thursday.

The plan, laid out in a notice that it intends to propose a rulein 2018, would undo a program by the Obama administration that benefits foreign couples where one person is working in the U.S. on an H-1B visa. The regulation is being challenged in court as an overstepping of executive authority, and the Trump administration appears to be signaling that it intends to overturn it rather than defend it.

The notice published on behalf of the Department of Homeland Security wasn’t specific about its reasoning, saying: “DHS is proposing to remove from its regulations certain H-4 spouses of H-1B nonimmigrants as a class of aliens eligible for employment authorization,” it said.

The H-4 is the visa issued to spouses of H-1B holders.

The notice said DHS was reviewing the Obama-era rule in light of President Donald Trump’s “Buy American and Hire American” executive order earlier this year.

In publishing the original rule allowing the work authorization in 2015, the Obama administration said it anticipated that the regulation would “support the goals of attracting and retaining highly skilled foreign workers.”

More than 41,000 of these work authorizations were approved in fiscal year 2016, and in fiscal year 2017, more than 36,000 were approved through June, according to government figures. The fiscal year ends in September.

Supporters of the program were dismayed by the notice.

“This announcement places into jeopardy thousands of hardworking, contributing individuals who have started their own businesses—and often have U.S. citizen children—who will needlessly be forced to revert to a status of inactivity,” said Leon Fresco, an immigration attorney who worked for the Obama administration.

Its critics say the spousal work authorization magnified the negative impact of the H-1B program on U.S. workers.

“There were no safeguards [in the spousal program] to make sure they weren’t displacing or undercutting U.S. workers,” said Jessica Vaughan, an immigration expert at the Center for Immigration Studies, which backs limits on legal as well as illegal immigration.

The Trump administration has signaled its intention to change a variety of regulations governing the legal-immigration system. In one example, the administration is considering eliminating another Obama-era regulation that aids foreign workers. The Optional Practical Training program allows foreign graduates from U.S. colleges in science and technology an extra two years of work authorization, giving them time to win an H-1B visa. The Trump administration could kill that benefit or reduce the two-year window, according to people familiar with the discussions.

Write to Laura Meckler at laura.meckler@wsj.com