The New York Daily News, the New York Post and Newsday each reported in Wednesday's editions that the video, uncovered by thesmokinggun.com, shows the 23-year-old Yankees pitcher making fun of Berra's diminutive stature.
"He might not be as tall as the front of your car," Chamberlain said of Berra to the Nebraska state trooper who arrested him.
Dave Kaplan, a spokesman for Berra, said that the 83-year-old former catcher was notified of what Chamberlain said, Newsday reported.
"He just totally laughed it off," Kaplan told Newsday. "He said it was all in fun. There was no offense taken whatsoever."
Chamberlain also says in the video that "opening a door and saying please and thank you" are not part of the norm in New York.
"The biggest thing that I've noticed driving here and there is if you let somebody in they open the window and say 'Thank you,' " he said of driving in Nebraska.
"In New York, they might hit you. Yeah, it's a joke."
Chamberlain also let the officer know he played for the Bronx Bombers.
"Obviously," he said, "I play for the Yankees."
Chamberlain pleaded guilty last week to drunken driving and was given nine months probation and a $400 fine. He also lost his driver's license for 60 days and has to complete an alcohol education class. After the plea deal, prosecutors dropped the second charge of driving with an open alcohol container.
He was pulled over Oct. 18 on the outskirts of Lincoln, Neb. Authorities say his blood-alcohol level was 0.134 percent. The legal limit in Nebraska is 0.08 percent.
According to the Post, Chamberlain had no comment on the video while taking a tour of the White House with the Yankees on Tuesday.