Speaking to New Idea's podcast The Royals in March, Ms Mollard said it was "well known" that Andrew enjoyed the company of multiple women.
"When Charles and Camilla reignited their relationship some years into his marriage to Princess Diana, he was forever known as the man who laid his wife down for the country," she said.
"This is really funny - Princess Anne, who we always think is the grumpy one with the bun... she had an affair with Andrew Parker-Bowles."
Ms Mollard further explained the two had remained friends thanks to their shared passion for horses, and when they meet each year at Royal Ascot they "get on really well".
Express.co.uk quoted royal author Penny Junor as supporting Ms Mollard's claim, writing in her biography on Camilla: "To the Duchess' fury, Andrew was also seeing Princess Anne, Charles' feisty younger sister."
Camilla married Andrew in 1973, and went on to have two children together: Tom and Laura.
The same year, Princess Anne wed Captain Mark Phillips and soon welcomed son Peter and daughter Zara, the Queen's eldest grandchildren.
Anne and Mark's marriage ended in divorce in April 1992.
Since December 1992, the Princess Royal has been happily married to Timothy Laurence.