Fisher had traveled to California on Saturday to visit his children and was visiting the house that Barnes shared with his estranged wife, Gloria Govan, the former star of the "Basketball Wives LA" reality show, sources said.
Barnes, who had concluded Grizzlies training camp in Santa Barbara, arrived at the house and a physical confrontation ensued on Saturday night, sources said. Barnes has known for "over a month" that Fisher is engaged in a relationship with his estranged wife, a source close to him told Yahoo Sports.
The New York Post first reported the altercation.
Barnes, 35, told friends that two people at the house – including a relative of his estranged wife – interceded on Fisher's behalf, sources told Yahoo Sports.
Barnes found Fisher, 41, in the backyard with Gloria and family members, and the altercation escalated from there, into the kitchen and then the home's front room, one witness said.
Fisher filed for divorce from his wife in March.
Fisher is considering legal action for the incident, sources said, but had not yet filed any charges.
The Knicks, Grizzlies and NBA security have been made aware of the incident and are expected to soon start working together on a probe of Saturday night's events. A significant part of the NBA's security department is overseas working closely on the league's preseason games in Europe, sources told Yahoo Sports.
"We are aware and currently gathering information regarding today's report involving Matt Barnes," the Grizzlies said in a statement.
Barnes had been with the Grizzlies at training camp in Santa Barbara, and Fisher had flown to Los Angeles on a Knicks off day over the weekend. Fisher missed the Knicks practice on Monday for what the team termed "a personal matter," but sources said that his failure to return to New York had to do with a malfunction on a private jet.
Fisher and Barnes had been friends and were teammates with the Los Angeles Lakers from 2010-12.
The Grizzlies and Knicks play Jan. 16 in Memphis and Feb. 5 in New York.