New York media reports said the brief rebuke occurred before the Yankees beat Kansas City 3-2.
Rivera was talking to reporters in the dugout about his "emotional" meeting with local fans earlier in the day, while Chamberlain was standing just outside the bench chatting with his family.
At one point, Rivera told Chamberlain to lower his voice. Once Rivera's interview was done, Chamberlain told Rivera in front of reporters: "Don't ever shush me."
Chamberlain then reiterated his message, saying he was serious about it.
On Sunday, Chamberlain said he and Rivera had joked and laughed about the incident after the game and again Sunday morning.
"It's just one of those things," Chamberlain said. "You're around someone all the time. He's a brother to me. I'm sure everyone's had an argument with a sibling at one time or another."
Rivera apologized to reporters that it wasn't taken care of behind closed doors, saying he wasn't mad at Chamberlain.
"I'm better than that," Rivera said.
Chamberlain, who said he approached Rivera after the game for an autograph for a friend, insisted there was no need for an apology and that it was "over with" and "done."
"Probably it's my fault personally," Chamberlain said. "There's a lot of things. My family's here. My son wasn't here which kinda bothered me. But that's another story for another day."
Information from ESPNNewYork.com's Wallace Matthews and The Associated Press was used in this report.