McNabb left NFL Network in 2013, but later lost a job with Fox Sports after pleading guilty to drunken driving in November 2015. Davis left the network in 2016, and appears frequently on Fox Sports; a spokesman there declined to comment. Weinberger left the network in 2015.

The lawsuit also said Cantor had been harassed by Warren Sapp, a former player and an ex-NFL Network analyst, as well as by Marc Watts, a former talent coordinator for the network. Sapp was fired from the network in 2015 after being arrested on charges of assault and soliciting prostitution.

“The supervisors knew about it, the supervisors observed it,” Cantor’s lawyer, Laura Horton, said in an interview on Monday. “It was insidious in this particular environment.”

NFL Network declined to comment beyond its initial statement announcing the suspensions. Weinberger, Taylor and McNabb did not respond to requests for comment; a representative for Faulk and Evans did not respond to a request for comment; Davis could not be reached for comment.

The network sent employees an email on Tuesday asking them not to comment on the allegations with anyone in the media, according to two people familiar with the email. And the N.F.L. is considering hiring an outside counsel to conduct an independent investigation, as Fox News did last year to investigate allegations of sexual harassment by the longtime network chief Roger Ailes, according to a person involved in the discussions who was not authorized to speak publicly about them.

All five players suspended had long and successful N.F.L. careers Faulk, a seven-time Pro Bowler who played for the Indianapolis Colts and the St. Louis Rams, won the Super Bowl with the Rams after the 1999 season and retired in 2007. Taylor spent his 12-year career with the Pittsburgh Steelers, winning two Super Bowl titles before retiring in 2015. Evans played for four teams across 10 seasons, winning a championship with the New Orleans Saints in 2010. He retired in 2011.

McNabb was a six-time Pro Bowler who played for three teams across a 13-year career, primarily with the Philadelphia Eagles, before retiring in 2013. Davis played for 13 years and four teams, retiring in 2003.