The 40 students in the class fled, with some tripping over seats as they ran from “what reasonably appeared to them as a credible threat of imminent classroom violence,” according to the lawsuit.

“I was near the door, and I started running out,” one student, Avery Kotler, told Annenberg Media, which reported on the stunt. “Everyone just left in a really big panic,” the student said.

In another incident, on Nov. 12, the two men stormed into a classroom dressed as characters from “Squid Game,” the violent Netflix series, according to the lawsuit. The men staged a fake kidnapping with two other associates who were not named in the suit, the filing said.

Mr. Bai asked for help from the professor, saying that “a bunch of people with weapons” were chasing him, the lawsuit said.

At one point, court documents say, Mr. Kanevsky and another individual chased Mr. Bai in the classroom as he yelled, “If they catch me, my family will die!” Before the incident, the fourth associate, who was not dressed up, had entered the classroom in order to make a video of the prank.

In the lawsuit, lawyers for the university said the men’s conduct “amounts to both a public and private nuisance,” adding that “it has caused students to experience emotional distress and genuine fear for their personal well-being” on campus.

Mr. Kanevsky has 111,000 subscribers to his YouTube channel, and Mr. Bai has about 3,000 to his channel. Both channels feature videos of pranks on the beach, at gyms and in stores.