He was released from jail on Saturday in Williamson County, Tenn. and charged with prevention of a 911 call. His bond was $5,000.
The Wright family issued a statement, through Wright's lawyer, on Sunday to NBC Sports Boston.
"On Friday night, Steven was arrested at our home following a verbal argument, and the police charged him with domestic assault," the statement said. "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 can still be disciplined by Major League Baseball under the term's of the league's domestic violence policy.
"We are aware of the incident involving Steven," the Red Sox said in a statement. "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, 33, was a second round pick by the Cleveland Indians in the 2006 June MLB Amateur Draft.
The University of Hawaii product made his first All-Star game last season after posting a 3.33 ERA and 13-6 record in 24 starts for the Red Sox. He made $593,000 this season and is eligible for arbitration in 2018. The righty posted a 1-3 record with an 8.25 ERA in five starts this season. He had surgery on his left knee in May.
Wright has a Dec. 21 court date.