Under a longstanding agreement with the city of New York, the museum must accept whatever patrons offer to pay.
But signs at cashier desks appear to demand full price, the suit contends.
The museum says its "recommended" policy has been place for 40 years and it makes no effort to deceive visitors.
The lawsuit, filed in New York City on behalf of former patrons, contends that the world famous museum, which receives six million visitors a year, uses misleading marketing and cashier training to deceive unwary visitors.
Lawyers say the signs in the lobby listing the price of admission with the word "recommended" below in smaller type violate a 1893 law mandating the public be admitted free of charge at least five days and two evenings per week in exchange for monetary grants and rent-free use of city-owned land.
The suit, which lawyers hope will eventually represent a broad class of people who have visited the museum in recent years, seeks a change in the admissions policy and reimbursement for those who they say were misled.
Confusion over whether visitors were required to pay the full $25 is "an issue with tourists travelling to the US from a foreign country", Michael Hiller, a lawyer for those who brought the suit, told the BBC.
"They are violating the statute, plainly and simply," Mr Hiller said, referring to the 1893 law. "The museum was designed to make art accessible to the public."
A former employee of the Met is expected to testify, Mr Hiller said.
The witness, who trained cashiers from 2007-2011, alleges that signage was changed from "suggested" to "recommended" because administrators believed it would encourage people to pay more, Mr Hiller said.
Harold Holzer, a spokesman for the museum, said the 1893 law had been superseded.
New York City agreed to the museum's request in 1970 to charge an admission fee - so long as the amount was left up to individuals and the signage reflected that.
About 40% of visitors pay full price, Mr Holzer said. He said gate proceeds allowed the Met to offer free admission to special exhibitions.
About 11% of the museum's operating expenses were covered by admissions last year. As a non-profit organisation, the museum pays no income taxes. It is one of the wealthiest museums in the world, with a $2bn investment portfolio.
Mr Holzer estimated the museum would receive 15-20% of its operating budget from the fees this year, with 11% coming from city grants.
The Met believes its policy "guarantees access for people regardless of their ability to pay", Mr Holzer said. He noted other New York City museums charge steep admission fees.
Entrance fees for prominent New York City art museums such as the Whitney, the Museum of Modern Art and the Guggenheim range from $18 to $25.
Mr Hiller demands the museum stop charging entirely for admission and remove the cashier desks.
"You have got to eliminate any effort to charge people," he said.
The Metropolitan Museum of Art's practice of requesting a "recommended" admission fee of $25 (Â£16) deceives patrons entitled to pay as little as they choose, a lawsuit charges.