On Monday, Kyrgios accused Zverev of being "selfish" after footage emerged of the German partying in Monte Carlo when he should have been isolating due to his involvement in the Adria Tour.
However, the Australian's stance did not go down well with six-time grand slam champion Becker, who wrote on Twitter: "Don't like no rats!
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"Anybody telling off fellow sportsman/woman is no friend of mine! Look yourself in the mirror and think your (sic) better than us..."
But it did not take Kyrgios long to defend himself and his right to question his fellow player's actions.
"For goodness sake Boris, I’m not competing or trying to throw anyone under the bus," the Australian replied.
"It’s a global pandemic and if someone is as idiotic as Alex to do what he has done, I’ll call him out for it. Simple."
Addressing the pandemic, Becker stated that "we should protect our families/loved ones and follow the guidelines but [I] still don’t like rats" as the pair continued to trade tweets.
The German called Kyrgios a "funny guy" after the Australian had labelled Becker a "bigger doughnut than I thought". Becker then insisted that he wanted to see the 25-year-old become "an incredible role model for the youth of the world".
World number seven Zverev committed to self-isolating last week following his involvement in the Adria Tour, which resulted in several players contracting the coronavirus.
Zverev said he and his team had tested negative but would self-isolate and undergo regular testing and apologised after he was filmed partying at a nightclub as part of the event.
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