The audio was captured during a live broadcast of practice sessions at Indian Wells, shortly after Andreeva left the court following a session with the American.
Pegula called the Roland Garros champion a "diva" and criticised the behaviour of her coach, Conchita Martinez.
“I think she’s a nice girl, but a bit of a diva. She needs to be more humble,” said the world No. 5, who is chair of the WTA Player Council. “The girl is super talented, but mentally she’s kind of… (gesture suggesting madness).”
“I like Conchita, but I’ve lost a bit of respect for her,” Pegula added, complaining that the coach does not keep Andreeva in line.
"If I were her coach and my player had just played four great games, she's up 4-0, she gets mad at me and chases me down... I'd tell her not to talk to me like that".
The WTA deleted the live streams from their YouTube channel, but because the practice session had been broadcast live, the recorded clip quickly spread across social media.
Pegula and Andreeva are in different groups at the WTA Finals. As a result, they can only meet on court if both players advance to the knockout stage.
The American is expected to face questions about the incident during the pre-tournament media sessions ahead of the opening matches scheduled for Sunday.