Wright was originally supposed to be in court Thursday after being arrested and charged with domestic assault Dec. 8.
Wright and his wife Shannon released a joint statement through his lawyer, saying the pair was "committed to working together to improve our relationship."
The case will be dropped if there are no additional offenses in the next 12 months.
According to a statement from the family released through Wright's lawyer to NBC Sports Boston after the arrest, the incident was "purely emotional" and Wright "did not raise his hand."
The Red Sox also issued a statement to NBC Sports Boston saying, "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."
The righthander appeared in only five games for the Red Sox in 2017 after going 13-6 with a 3.33 ERA and making the All-Star team in 2016.