Swihart has left the team to be with his family, according to the Red Sox.
"We are saddened to confirm the passing of Red Sox catcher Blake Swihart's 23-year-old brother, Romell Jordan," the team said in a statement. "The entire Red Sox organization sends its deepest condolences to the Swihart family for their loss. The family is asking for privacy at this difficult time."
No details about Jordan's death have been released.
Earlier Wednesday, Red Sox manager Alex Cora said a team member was dealing with a "family emergency." The team also canceled media availability, other than Cora's comments.
Red Sox pitcher David Price appeared to address the situation in a tweet Wednesday morning.
While struggling with family problems, Jordan was taken in by Swihart's family during his final two years in high school.
This is the second death the Red Sox have dealt with during spring training. Boston Globe reporter Nick Cafardo died Thursday after collapsing outside the team's spring training clubhouse. He was 62.
Jordan rushed for 551 yards with five touchdown in three seasons with the Lobos from 2014 to 2017. He missed the 2016 season with an ACL injury.