Wright's family issued a statement to NBC Boston through Wright's lawyer, Alex Little.
"On Friday night, Steven was arrested at our home following a verbal argument, and the police charged him with domestic assault. Although he said things he deeply regrets, he did not raise his hand at anyone during the incident, and the situation was purely emotional. We are working together as a family to make our relationships stronger, and we ask that you respect our privacy as we do so."
Wright, who was also charged with prevention of a 911 call, was released Saturday morning on $5,000 bond.
MLB has begun investigating the domestic assault charges against Wright, a source told ESPN's Scott Lauber. The commissioner's office has independent authority to review such matters under its joint domestic violence policy.
MLB suspended New York Yankees closer Aroldis Chapman for 30 games in 2016 even though criminal charges weren't filed against him. Catcher Derek Norris was banned for the final month of the 2017 season after allegations of physical and mental abuse by his ex-fiancée.
Wright, a right-handed knuckleballer, made the All-Star team in 2016 but has been plagued by injuries since. His '16 season ended after he injured his shoulder as a pinch runner, and last season he made just five starts because of a knee injury that required surgery.
The Red Sox released the following statement to reporters: "We are aware of the incident involving Steven. This is certainly a matter that the Red Sox take very seriously. It is my understanding that both local police and Major League Baseball are looking into this, and for that reason, the club won't have any further comment at this time."
Wright is subject to discipline under the terms of Major League Baseball's domestic violence policy. MLB has begun investigating the charges.
Red Sox president of baseball operations Dave Dombrowski said any baseball-related punishment for Wright is in MLB's hands.