They state the show was meant to start at 20:30 EST on all three nights, but in each case, it did not begin until after 22:30, ending around 01:00.
The case says they “would not have paid for tickets” had they known it would finish so late.
The BBC has asked Madonna, Live Nation, and the Barclays Center for comment.
The case, brought by Michael Fellows and Jonathan Hadden, states that “many ticketholders who attended concerts on a weeknight had to get up early to go to work and/or take care of their family responsibilities the next day”.
They are suing promoter Live Nation and venue the Barclays Center for “false advertising, negligent misrepresentation, and unfair and deceptive trade practices.”.
Mr Fellows and Mr Hadden attended the show on Wednesday, December 13, 2023, but the legal documents note that other nights at the same venue, on December 14 and 16, also reportedly started more than two hours late.
“Defendants failed to provide any notice to the ticketholders that the concerts would start much later than the start time printed on the ticket and as advertised, which resulted in the ticketholders waiting for hours,” the document state.
The court papers also say Madonna “has a long history of arriving and starting her concerts late, sometimes several hours late”, citing examples including “her 2016 Rebel Heart Tour, her 2019-2020 Madame X Tour, and prior tours, where Madonna continuously started her concerts over two hours late”.
The plaintiffs are suing for unspecified damages.
This is not the first time fans have objected to the singer being late for her shows, and in 2019, a fan sued over a delay for a US show, but he voluntarily dismissed the case a month later, according to ABC News.
In the same year, Madonna had shared a post of her live on stage, in which she told fans: “There’s something that you all need to understand. And that is, that a queen is never late.”