It’s Taylor Swift’s world. The government is just suing Ticketmaster in it.

When Attorney General Merrick Garland, a devoted Swiftie, announced the antitrust case against the merged companies Thursday, he dropped a reference to the singer in his remarks.

“It is time to break up Live Nation Ticketmaster. The American people are ready for it," Garland said in a shout-out to the Swift song “Ready for It?"

In 2022, the presale for tickets to Swift’s “Eras Tour" was hobbled by a Ticketmaster computer-system meltdown, leaving millions of Swifties heartbroken about missing a chance for an early ticket. The debacle spurred interest in an investigation the Justice Department had already started and underscored Ticketmaster’s role as the gatekeeper to most major live-music experiences.

State officials who joined the federal government’s lawsuit made their own efforts to connect the legal move to Swift’s tour and the plight of her fans. The state law enforcers “relentlessly sought justice" for fans hurt by Live Nation’s alleged monopoly “since Ticketmaster’s Taylor Swift ticketing debacle in 2022," Tennessee Attorney General Jonathan Skrmetti said in his own statement on the case.

The Justice Department’s suit against Live Nation and Ticketmaster is much broader than Swift’s ticket troubles. It takes aim at Live Nation’s role as the dominant promotion and ticketing company in the business and tees up a legal battle that has the potential to redistribute power in the live-events business and change how consumers buy tickets.

The lawsuit, joined by more than two dozen states, alleges that Live Nation used its power to squelch competition and retaliate against promoters and venues that threatened its dominance. The company uses exclusive contracts to lock out rivals, driving prices and fees higher for fans, said the department, which is asking a court to break up the company.

Live Nation rebutted the lawsuit’s allegations. It said the government ignores the real causes of higher ticket prices: the ability of superstar artists to set ticket prices, secondary sales of tickets that can drive prices far higher and rising production costs.

The problems with Swift’s “Eras Tour" ticket sales in 2022 were caused by a novel cyberattack that involved bots bombarding its systems in pursuit of tickets they could resell, the company said. Live Nation ultimately was able to resume selling tickets after suspending sales for part of the day.

Swift’s name doesn’t appear in the lawsuit against the companies, which merged in 2010 despite concern about whether the deal would create an impenetrable monopoly. But a statement in the court complaint about how “product quality and stability suffer" when competition is lacking does refer to the ticket incident, among other snafus, people familiar with the matter said.

Swift was clearly on the mind of Justice Department officials who appeared at the news conference to announce the lawsuit.

The legal action is an attempt at “making this era of live music more accessible for the fans," Lisa Monaco, the department’s second in command, said at the press conference.

New York Attorney General Letitia James liberally drew from Swift and other artists in her commentary. “When companies like Live Nation control every aspect of an event, it leads to bad blood—concertgoers and sports fans suffer and are forced to pay more," James said. “Bad Blood" is a Swift single released in 2014.

Jonathan Kanter, who leads the Justice Department’s antitrust division, was the only senior federal official who didn’t quote Swift in his remarks about the case. Kanter, who plays guitar for a hobby and has a recording studio in his Maryland home, instead evoked a Beatles tune as he talked about defending the role live music plays in people’s lives.

“It is here, there and everywhere," he said.

So was Swift. Some members of the department’s press office who stood on the sidelines of the news conference wore the friendship bracelets that are popular among Swifties.

But, like Swift, none of the beaded accessories made it to the stage with Garland.

“No members of leadership were wearing friendship bracelets," a department spokeswoman said.

Sadie Gurman, Jan Wolfe and Erin Mulvaney contributed to this article

Write to Dave Michaels at dave.michaels@wsj.com