"If I had played my cards right, I could have been the first Jewish princess," she reportedly told the audience.
Streisand even showed newspaper headlines referencing her alleged fling with 70-year-old Charles, who once said the singer was his "only pinup."
One headline shown read, "Barbra charms her prince, Charles."
Streisand first met Charles in 1974 on the set of "Funny Lady."
They met again 20 years later when she sang for the Prince's Trust charity at London's Wembley Stadium.
In 2006, the biography "Barbra - The Way She Is" alleged that Charles tried to romance Streisand in November 1994 when he was separated from the late Princess Diana and dating Camilla Parker-Bowles.
Charles wasn't the only royal the "Yentl" star spoke of at her show on Sunday.
In her opening number, Streisand amended a lyric to "When the Sun Comes Out" to "When the sun begins to sparkle, like that ring on Meghan Markle."