Eighteen former National Basketball Association players have been indicted on charges they participated in a conspiracy to defraud an N.B.A. health care plan of nearly $4 million, the federal authorities said on Thursday.

The scheme lasted from at least 2017 through last year and involved the submission of fraudulent claims for reimbursement of medical and dental services that had not actually been provided, according to a federal indictment unsealed in Manhattan.

For the most part, the 18 former players charged in the scheme played in the N.B.A. in the late 1990s and the 2000s. Two of the most notable are Ronald Glen Davis, nicknamed “Big Baby,” and Tony Allen, both of whom played on the Boston Celtics team that won the N.B.A. championship in 2008.

Mr. Allen, now 39, was one of the league’s best defensive players during his career and is scheduled to have his number retired by the Memphis Grizzlies, where he played seven seasons, next year.

Others charged included promising prospects whose careers did not reach the heights that had been expected, including Darius Miles and Sebastian Telfair, both of whom were drafted out of high school.

The indictment said that one of the former players, Terrence Williams, who played for the New Jersey Nets and the Houston Rockets, had orchestrated the scheme and recruited other former players by offering to supply them with false invoices to support their fraudulent claims. The indictment charges that Mr. Williams also received $230,000 in kickbacks in the scheme.

The conspirators submitted claims totaling $3.9 million, and they ultimately received about $2.5 million in fraudulent proceeds, according to the indictment.

The charges were announced in New York on Thursday at a news conference held by Audrey Strauss, the U.S. attorney for the Southern District of New York, and Michael J. Driscoll, the head of the F.B.I.’s New York office.

Ms. Strauss said that the investigation was ongoing.

Several of the players charged played at least part of their career for New York-area teams, including Shannon Brown with the Knicks, and Mr. Williams, Antoine Wright and Chris Douglas-Roberts with the Nets.

Others gained fleeting instances of fame, like Milton Palacio, who in 2000 hit a memorable buzzer beater against the Nets, and Ruben Patterson, who was said — perhaps apocryphally — to have called himself the “Kobe Stopper,” for his purported ability to slow down the Los Angeles Lakers superstar Kobe Bryant.

Mr. Telfair, a cousin of the former N.B.A. star Stephon Marbury, graced magazine covers as one of the best high school players in the country when he played at Brooklyn’s Lincoln High School in the early 2000s. But he was dogged by legal troubles related to weapons during his professional career, which included early stints with the Portland Trail Blazers and the Celtics.

In 2008, Mr. Telfair pleaded guilty to illegal handgun possession and was sentenced to three years probation. In 2019, he was sentenced to 3.5 years in prison for gun possession, this time stemming from an arrest two years earlier, when he was found with four loaded guns and a bulletproof vest.

Sopan Deb contributed reporting.