The right-hander will not appeal.
The Red Sox were hopeful Wright would be ready to open the season on time after recovering from right knee surgery last year. His absence cements a spot in the rotation for left-hander Brian Johnson.
MLB investigated a Dec. 8 incident involving Wright and his wife, Shannon. He was arrested at their Tennessee home on misdemeanor charges of domestic assault and preventing a 911 call. He was released the following day on a $2,500 bond, and his case was later retired by the Williamson County court and will be dropped if additional offenses don't occur within the next year.
Wright and his wife have been undergoing counseling since.
"While it's clear that Mr. Wright regrets what transpired that evening, takes full responsibility for his actions and has committed himself to treatment and counseling components of the [MLB domestic violence] policy, I have concluded that Mr. Wright's conduct on Dec. 8 violated the policy and warrants discipline," commissioner Rob Manfred said in a statement.
In a separate statement released by the players' union, Wright reiterated comments he made early in spring training when he insisted he "did not make physical contact with my wife. The legal case that was retired supports that claim."
Wright also said he regrets his actions and takes full responsibility. His decision not to appeal the suspension was made "in an effort to move forward and focus on my family and returning from injury," the pitcher said. He also apologized to the Red Sox, teammates, fans and his family and expressed gratitude for their support.
Wright's suspension matches last year's 15-game punishment for New York Mets closer Jeurys Familia. Other violators of the domestic violence policy, including New York Yankees closer Aroldis Chapman (30 games) and Mets infielder Jose Reyes (52 games), received longer suspensions.
"While we are disappointed that this incident occurred, we are encouraged that Steven is taking meaningful steps to learn from this unfortunate incident," the Red Sox said in a statement.