Police in New Canaan, Connecticut, said officers responded to investigate a "family dispute" involving the singers on Saturday night.
The 72-year-old Simon and 47-year-old Brickell were released and an arraignment is scheduled for later in Norwalk.
Simon is a 12-time Grammy award winner and member of The Songwriters Hall of Fame and Rock n' Roll Hall of Fame - as half of the duo of Simon and Garfunkel and as a solo artist.
He and Brickell were married in 1992.
Police chief Leon Krolikowski said at a news conference that a caller from the singers' home had dialled police on Saturday night and hung up.
Officers who responded found minor injuries and believed it was a case of domestic violence, he said. He did not say who was injured.
Simon and Brickell, who have been married for more than two decades, were each given a misdemeanor summons and one of them agreed to leave and go to another location, Mr Krolikowski said.
"There was aggressiveness on both sides," he said. "They're both victims and they have children involved and we're trying to be very cautious of that."
Last month, Simon wrapped up a tour of the US with Sting. Most recently, he performed at the 25th anniversary of the Rainforest Fund benefit concert in New York on April 17.
Brickell is perhaps best known for the song What I Am, recorded with her band the New Bohemians and released in 1988.
She collaborated last year with comedian Steve Martin, who has an acclaimed career as a folk musician, for the roots album Love Has Come For You.
The pair won a Grammy for best American Roots song in January. The two are touring and are due to perform next on May 9.
An lawyer for Simon and Brickell said the incident that led to them being arrested was "much less than nothing".
Allan Cramer said, at Norwalk Superior Court, that he is representing both singers. He said the two get along fine and have never had problems like this.
Cramer said that on a scale of one to 10 the injuries involved in the dispute were a "one".