BBC News reports Ticketmaster was recently forced to cancel the main sale of tickets on its website, leaving many fans frustrated.
The lawsuit, filed by 26 'Swifties' from across the country, alleges that the company is guilty of fraud, price-fixing and anti-trust violations.
Ticketmaster has yet to comment on the filing.
The November sale of Swift tour tickets was marred by several issues, with some fans later reporting that access codes meant to deter bots didn't work properly and that tickets were being re-sold at higher prices online while the sale was still going on. The company's website also crashed repeatedly amid extremely high demand.
According to the lawsuit, filed in California, Ticketmaster and its parent company, Live Nation, imposed artificially high pre-sale, sale and re-sale prices on fans. The suit claims an "intentional deception" that allowed third-party scalpers to buy the vast majority of tickets.
It also claims that Ticketmaster is a "monopoly that is only interested in taking every dollar it can from a captive public".
In November, the company said that 3.5 million people registered in advance as "verified fans" in the hopes of getting tickets for Swift's 52-city US "Eras Tour" next year.
Soon after, it said that a "staggering numbers of bot attacks" and "historically unprecedented demand" had overwhelmed its website.
Just hours after the sale began, tickets were being sold on re-sale websites for prices of up to $22,000 (£17,950).
The Swift fans are seeking $2,500 for each alleged violation - a sum that could potentially amount to millions.
"Millions of fans waited up to eight hours and were unable to purchase tickets as a result of insufficient ticket releases," the lawsuit claims. "Ticketmaster intentionally provided codes when it could not satisfy demands."
Additionally, it says that artists, including Swift, "have no choice" but to work with the company "because no other venue can hold half as many people as the stadiums and venues working through 'Ticketmaster'".
Ticketmaster has not publicly commented on the lawsuit, but has previously apologised to fans for a "terrible experience" as they tried to buy tickets. The BBC has reached out to the company for additional comment.
In a November statement posted after Swift tour ticket sales were cancelled, Live Nation said that it "takes its responsibilities under the anti-trust laws seriously" and doesn't "engage in behaviors that could justify anti-trust litigation, let alone orders that would require it to alter fundamental business practices".
Swift has said it was "excruciating" to watch fans struggle to get tickets.