By Brent Kendall 

The clash over protecting a free-flowing Internet while also fighting online piracy has shifted to an unlikely and largely unknown setting: a legal battle about teeth-alignment devices at a federal trade body.

A U.S. appeals court this month will consider whether federal tariff law gives the International Trade Commission the power to order a halt to foreign digital transmissions into the U.S. when those communications infringe U.S. intellectual property. Traditionally, the ITC has intervened only to stop the importation of physical goods.

In a proceeding closely watched by tech companies and the movie, music and publishing industries, the commission expanded its approach last year while reviewing a trade dispute over orthodontic devices. The ITC decided it could take action against virtual material coming into the U.S. and ordered a Texas-based company, ClearCorrect, to stop receiving digital models and data from Pakistan for the manufacture of teeth aligners, invisible mouthpieces used as an alternative to braces.

The ITC had said ClearCorrect was infringing patents held by larger rival Align Technology Inc., a San Jose, Calif., company that generated more than $700 million in revenue last year from its Invisalign devices.

The U.S. Court of Appeals for the Federal Circuit will hear arguments on ClearCorrect's appeal in Washington on Aug. 11.

The Internet Association, a trade group representing companies like Google Inc., Amazon.com Inc. and Yahoo Inc., opposes the ITC's approach, saying it could disrupt the global Internet and interfere with cloud-computing networks, where data is stored in centers all around the world.

The current case is about patents, but the ITC also can take action against goods that infringe copyrights, an issue important to Hollywood and other rights holders. They are eyeing the ITC as a new venue for combating foreign websites that trade in pirated digital material and the ability of U.S. consumers to access them.

The ITC's mission of protecting U.S. companies from imported goods that infringe on intellectual property "matches up well with some of our current problems," said Dan Robbins, a senior attorney with the Motion Picture Association of America, which filed a legal brief with the Recording Industry Association of America in support of the ITC in the ClearCorrect case.

If the commission's jurisdiction "is limited to just physical goods, the ITC will end up in the historical dustbin because everything these days is moving toward electronic importation," Mr. Robbins said.

Allan Adler, general counsel for the Association of American Publishers, said if the ITC's digital jurisdiction is upheld, "we would certainly be exploring it more seriously." The commission could be "an ancillary or alternative to litigation in federal court," said Mr. Adler, whose group also is backing the ITC in the case.

The ITC process allows companies to file complaints alleging they are being harmed by illegal imports. The only remedies available to the commission are to exclude imports and to order companies to cease-and-desist from selling or distributing infringing goods. Companies using the process for physical goods often file related lawsuits in federal court seeking monetary damages and injunctions against infringing activity.

As the teeth case has gained steam, open-Internet advocates have raised concerns about expanded ITC powers.

Charles Duan of the public-interest group Public Knowledge, which filed a friend-of-the-court brief opposing expanded ITC authority, said the debate resembles the battle in 2011 and 2012 over the Stop Online Piracy Act. That bill was important to the entertainment industry but lawmakers abandoned it when Internet companies waged an opposition campaign, saying the legislation would stifle the Web and burden free speech.

"The concern is that the ITC is opening the door to Internet site-blocking, the policy that killed SOPA," said Mr. Duan, director of Public Knowledge's patent reform project. "Blocking data transmissions based on their content cuts against the general principles of the openness of the Internet, which has been a foundation of its success."

The Internet Association agrees. "The ITC believes it can use patent law to regulate all electronic data entering the U.S. We believe the Commission's position is unlawful, unenforceable and harmful to global Internet commerce," said Abigail Slater, the group's vice president of legal and regulatory policy.

Aside from the piracy issue, the case highlights the importance of digital goods in an age where products can be built with 3-D printers.

ClearCorrect's manufacturing process starts with a physical model of a patient's teeth in the U.S., which is scanned digitally. The file is uploaded and received by technicians in Pakistan who create virtual models of a patient's teeth moving into straight positions. The files are transferred back to the U.S. electronically, where ClearCorrect prints 3-D models that are used to make aligners.

The ITC in court papers said ClearCorrect hoped to skirt U.S. patent law by farming out part of its process to Pakistan. The commission argues it would be unreasonable to say it could block physical dental molds at the border yet do nothing to stop digital ones.

An ITC spokeswoman said the agency wouldn't comment further, citing current litigation.

ClearCorrect lawyer Michael Myers denied the company was infringing patents and said it had good reasons for outsourcing part of its process overseas. Creating digital orthodontic models is a labor-intensive process "and labor is cheaper" in Pakistan, he said.

Mr. Myers said Align Technology and its entertainment industry backers were seeking to push the envelope by nudging the ITC into digital commerce. "If this was such an important tool to fight online piracy, why haven't they used this mechanism? It's because it hasn't been available," he said, adding Congress should be the body to extend that power.

Align didn't respond to requests for comment. In a court brief, the company said the ITC was targeting only the specific actions of ClearCorrect and wasn't installing itself as a new government regulator of U.S.-bound Internet transmissions.

"The commission no more regulates electronic carriage of articles into the U.S. than it regulates traditional carriage of goods into the U.S. by ship, railroad, or truck," it said.

Write to Brent Kendall at brent.kendall@wsj.com