There are no immediate details available on the incident, but a phone call was placed to police at about 8 p.m Saturday night.
The couple, who live in New Canaan, Conn. and who have been married for more than 20 years, are scheduled to appear in Norwalk Superior Court on Monday morning.
The 72-year old 12-time Grammy winner won a Grammy Lifetime Achievement Award in 2003 for his work in the duo Simon and Garfunkel.
Brickell, 48, was the lead singer of the 1980s folk band Edie Brickell & New Bohemians.
Update: More details from the Associated Press:
A caller from the singers' New Canaan home dialed 911 Saturday night and hung up, police chief Leon Krolikowski said at a news conference Monday. 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, 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."
Late update: One police officer described the incident as “your typical dispute. Some yelling and screaming and pushing. If it wasn’t the name, it wouldn’t be this kind of deal.”
An attorney representing both Simon and Brickell told the Associated Press that on a scale of one to 10, the injuries involved in the dispute were a "one."
This post has been updated.