Mr Musk’s remarks came after the Wall Street Journal reported that his friendship with Mr Brin had come to an end due to the alleged romance.
Mr Musk called the news “complete bs” in response to a link to the story posted on Twitter.
Mr Musk went on to explain that he and Mr Brin are still friends and that they were “at a party together last night!”
According to persons familiar with the situation, Mr Musk had a brief affair with Ms Shanahan late last year, according to the Wall Street Journal.
This drove Mr Brin to file for divorce early this year, thereby ending the two high-profile technology millionaires’ long friendship, according to the article.
Mr Brin and his wife were separated but still living together at the time of the alleged affair in December, according to a person close to Ms Shanahan, according to the Wall Street Journal.
Mr Musk stated in a separate tweet, “WSJ [Wall Street Journal] has written so many bs hit pieces on me and Tesla that I’ve lost count.”
Despite having a prenuptial agreement, Mr Brin and Ms Shanahan are currently negotiating a divorce settlement that might be worth up to $1 billion (£830 million), according to the tabloid.
According to her LinkedIn profile, Ms Shanahan is a California-based attorney and the creator of the legal technology company ClearAccessIP as well as the Bia-Echo Foundation.
The Bia-Echo Foundation is a charitable organisation dedicated to “reproductive longevity and equity, criminal justice reform, and a healthy and livable world.”
Mr Musk, who also runs rocket company SpaceX, is now locked in a legal battle over his failed bid to buy Twitter for $44 billion.
The social networking platform sued him earlier this month after he announced his withdrawal from the proposed takeover of the company.
According to the Bloomberg Billionaires Index, Mr Musk is the world’s richest individual, with an estimated fortune of more than $240 billion.
According to the same rating, Mr Brin is worth roughly $95 billion, ranking him seventh in the world.
Ms Shanahan, Mr Brin, and Google did not react promptly to demands for comment from the BBC.