The list of American entities caught in rising tensions between China and the United States is growing: Nike, Apple, Gap and the National Basketball Association, to name a few.

Now add another: the Eastman Philharmonia, a group of more than 80 student musicians at the Eastman School of Music in Rochester, N.Y.

The school, part of the University of Rochester, this week canceled a planned tour of China after three South Korean members of the orchestra were unable to obtain visas, apparently in retaliation for South Korea agreeing in 2016 to deploy an American missile defense system.

While there is no official ban on South Korean artists in China, many have had difficulties performing there in recent years because of tensions over the defense system, which China has angrily opposed as a threat to its own security.

Eastman had initially said it would go forward with the tour, despite the exclusion of the South Korean students. But after an outcry by students and alumni, with some accusing the university of bowing to China, the school reversed course.

“The best course of action for the Eastman community and the values we share is to wait until the Philharmonia can perform as one,” Jamal J. Rossi, the dean of the school, wrote in a letter to students, faculty and alumni on Tuesday.

The cancellation has highlighted the roiling tensions at the center of the United States-China relationship, as the two countries compete for military and economic influence and fight a trade war.

Chinese leaders have grown more assertive in recent months in pushing foreign entities to play by Communist Party rules. The government unleashed a campaign against the N.B.A. this month, for example, after the general manager of the Houston Rockets expressed support for antigovernment protests in Hong Kong.

Eastman’s visa problems appeared to reflect China’s continuing efforts to punish the United States and South Korea for the missile system, known as the Terminal High Altitude Area Defense system, or Thaad.

A wave of nationalistic sentiment broke out in China in 2017 as the system neared completion. South Korean artists were also caught in the fray, with K-pop stars, opera singers and actors forced to cancel events in China.

Tensions over the missile system have faded from public view more recently. But the denial of the visas suggests Chinese officials are still looking for ways to show anger over American and South Korean military policy, experts said.

“I was surprised Beijing would go to such lengths to punish classical musicians for a missile defense system,” John Delury, an associate professor of Chinese studies at Yonsei University in Seoul, South Korea, wrote in an email. “Not a great look!”

The Chinese Foreign Ministry suggested on Wednesday that the visa denials were not related to the missile system, as Eastman administrators have said.

Geng Shuang, a ministry spokesman, said that he was not aware of the Eastman case but that it was most likely an isolated incident. He said that more than four million South Koreans visited China last year.

“If, as people say, we are refusing to issue visas to South Koreans due to the Thaad issue, how did these several millions of people come?” Mr. Geng said at a regular news briefing in Beijing.

The denial of the visas, which school officials said they learned about in late September, brought heated debate to Eastman, a renowned music school.

Students and alumni said that by originally going ahead with the tour, the school seemed more concerned about economic opportunities in China instead of the well-being of students. Many American orchestras have turned to China in recent years as ticket sales in the United States have slowed.

Before he changed course, Dr. Rossi, the dean, acknowledged in a letter that canceling the tour could hurt the school’s reputation in China. But he denied that money had played a role.

“This decision was not made under the influence of profit, of which there is none,” he said in a letter last week.

Eastman, like other American music schools, has been increasingly reliant on students from abroad, including both South Korea and China. Its website says that international students make up a quarter of it student body.

Others said the school should have done a better job planning and should have been aware of potential visa problems facing South Korean artists. They criticized school administrators for initially agreeing to go forward without the South Korean students.

“It speaks to their own botched planning that the visa issue was not anticipated,” said Diana Rosenblum, a Ph.D. student in music composition at Eastman. “The exclusion of the South Korea students, both on principle and under the school’s own policy on nondiscrimination, should never have been a choice in the first place.”

Other American orchestras have faced similar problems, according to Leonard Slatkin, a prominent conductor who is the music director laureate of the Detroit Symphony Orchestra.

Mr. Slatkin said that seven South Korean members of the Detroit orchestra were initially denied visas in 2017 before a planned tour in China. The Chinese government eventually relented, Mr. Slatkin said, but not until he had threatened to cancel the trip.

“Discrimination should never ever be acceptable at any level,” Mr. Slatkin wrote in an email. “My hope is that Eastman will continue to seek a solution so the all the young musicians can go.”