Simon told a Superior Court judge in Norwalk, Connecticut, he had a rare argument with his wife on Saturday night at their home.
The couple, who have been married for 22 years, held hands and said they did not feel threatened by each other.
"We're fine. We love each other. We're fine. We had an argument. It's over," Simon said as he left the courthouse.
Continue reading the main storyThese people have had a wonderful life together and they've never had these types of problems”End Quote Alan Cramer, lawyer for Paul Simon and Edie Brickell "We're going to go back home today. We're going to watch our son play baseball," he added.
"Neither one of us has any fear or any reason to feel threatened."
'Wonderful life'The arrest came on Saturday night after a caller from the singers' home phoned the emergency services and hung up, police chief Leon Krolikowski said at a news conference on Monday.
Officers who responded found minor injuries and believed it was a case of domestic violence, he continued. He did not confirm who was injured.
"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."
Paul Simon told reporters he would be returning home with his wife Simon and Brickell were each given a misdemeanour summons. One of them - again unspecified - agreed to leave and go to another location.
The singers' lawyer, Alan Cramer, dismissed the severity of the argument, calling it a "one on a scale of one to 10".
"They are here together, they get along fine with each other," Cramer told reporters before the court hearing.
"If it were Joe Blow we wouldn't be here. You certainly wouldn't be here. These people have had a wonderful life together and they've never had these types of problems."
Paul Simon's hits include You Can Call Me Al and Me and Julio Down by the Schoolyard 
Edie Brickell appeared with her band on Top Of The Pops in 1989, as What I Am reached 31 in the charts Simon, 72, first found fame as one half of folk duo Simon and Garfunkel, while Brickell, 48, was the lead singer of Edie Brickell & New Bohemians.
The band scored an international hit with their debut single What I Am in 1988, a track subsequently covered by former Spice Girl Emma Bunton in 1999.
Earlier this year, Brickell won a Grammy award with comedian Steve Martin for best American roots song, Love Has Come For You.
She is due to start touring in May with Martin and the Steep Canyon Rangers.
Edie Brickell has three children with Paul Simon Simon is a 12-time Grammy winner and member of the Rock and Roll Hall of Fame - both as part of Simon and Garfunkel and as a solo artist.
He recently finished a joint tour with British musician Sting and last year performed a benefit concert in the couple's hometown of New Canaan, performing songs including The Sound of Silence and Mrs Robinson.
According to local media, the couple have lived in the Connecticut town with their three children for a number of years.
They have been asked to return to court on 16 May.
