The subpoenas are related to criminal and civil investigations examining whether anyone in the government illegally passed along nonpublic information about the health policy that ended up in the hands of traders, according to people briefed on the matter. The probe was sparked by a 2013 Wall Street Journal report that detailed how health-insurance stocks jumped moments before the government announced news favorable to those companies relating to Medicare payments.

The stock surge was prompted by an email sent by a Washington-based policy-research firm that predicted the change for its Wall Street clients. That alert, in turn, was based in part on information provided to the firm by a former congressional health-care aide turned lobbyist, according to emails reviewed by the Journal.

The activity surrounding the federal grand jury wasn’t previously known and signals that prosecutors haven’t given up on the matter.

It is highly unusual for federal law-enforcement officials or securities regulators to issue subpoenas to members of Congress or their aides, given sensitivities and legal barriers connected with the separation of powers between the branches of government. These subpoenas are the first formal requests for information to Congress involving a federal insider-trading investigation in nearly a decade.

The subpoenas suggest prosecutors are seeking information from officials in the U.S. House as they try to track how information about the policy moved between Wall Street and the Centers for Medicare and Medicaid Services, the agency in question. The investigation had previously focused on health-care aides in the Senate, according to people briefed on the matter.

Mr. Camp declined to discuss the investigation except to confirm receipt of the subpoenas. “I’m not going to comment on details or what may or may not be happening on the committee,” he said in a brief interview. A committee spokesman declined to comment on behalf of the subpoenaed staffer.

A spokesman for the SEC declined to comment as did a spokeswoman for the Southern District of New York.

It isn’t known whether Mr. Camp or officials with the Ways and Means Committee agreed to provide information to investigators or whether they are targets of the investigation or witnesses. Attorneys for the U.S. House met earlier this month with SEC officials to discuss the subpoenas, according to people involved in the matter.

CMS launched its own investigation into whether officials there improperly leaked word of the policy change. A spokesman for the agency said its investigation has been referred to the Department of Health and Human Services, of which CMS is a part, which declined to comment.

The information given to the Washington research firm, Height Securities, came from a lobbyist named Mark Hayes. Mr. Hayes, who was a top health-care aide in the Senate before he became a lobbyist, said in an April 1, 2013, email that he had learned of the change from “very credible sources,” according to a copy of the email reviewed by the Journal. Lawyers for Mr. Hayes and Height Securities declined to comment for this article.

Federal prosecutors and SEC investigators have spent more than a year seeking to identify who those “credible sources” were and to determine whether they broke insider-trading rules. It would be illegal if someone in the government leaked word to Wall Street traders or to anyone seeking information on behalf of investors.

Mr. Hayes told congressional investigators he didn’t receive a tip from a single individual. He said he made his prediction based on information he gathered partly from conversations with a Senate aide and his own analysis, the Journal reported last year, based on information from Senate investigators.

The investigation is part of a new focus by SEC and law-enforcement officials into possible violations of securities rules involving trades based on information about government policy.

Federal securities regulators have been eager to bring an insider-trading case against a government official since a 2012 law made clear that members of Congress and congressional aides have a legal duty not to share nonpublic, market-sensitive information with Wall Street, according to securities lawyers.

“The SEC recognizes that the strongest deterrent message to Hill staff will be in an insider trading case,” said Jacob Frenkel, a partner at law firm Shulman Rogers and a former SEC enforcement attorney.

—Jean Eaglesham and Charles Levinson contributed to this article.

Write to Brody Mullins at brody.mullins@wsj.com and Andrew Ackerman atandrew.ackerman@wsj.com