Police were called to the couple's New Canaan residence to investigate a family dispute after a 911 hang-up call was received. There were minor injuries, according to police.
Simon and Brickell were charged with one count each of disorderly conduct. They were released on their own recognizance to appear in court on Monday.
The couple appeared in court Monday holding hands. Simon told the judge he had a rare argument with his wife. Neither requested an order of protection.
"He's no threat to me at all," Brickell told the judge.
"We're going to go home. We're going to watch our son play baseball," Simon added.
The couple is due back in court on May 16.
Paul Simon achieved fame in the 1960s as one half of Simon and Garfunkel, and has had continued success in his solo career. Brickell was the lead singer for her group the New Bohemians, who had the hit "What I Am" in 1988.
Simon is a 12-time Grammy winner and member of The Songwriters Hall of Fame and Rock and Roll Hall of Fame, as half of the duo of Simon and Garfunkel and as a solo artist.
Simon, 72, and Brickell, 47, were married in 1992 and have three children together.
The Associated Press contributed to this report.