Paul experienced a medical emergency Tuesday morning at the team's facility and was rushed to the hospital.
The cause of his death has yet to be determined.
"The loss of a family member is a tragedy, and Markus Paul was a loved and valued member of our family," team owner Jerry Jones said in a statement. "He was a pleasant and calming influence in our strength room and throughout The Star."
Paul was hired as the team's strength and conditioning coordinator prior to the season and promoted to coach earlier this year. He first joined the Cowboys in 2018 as an assistant strength coach.
Paul was a part of five Super Bowl-winning teams over his time as a coordinator with the New England Patriots from 2000 to 2004 and an assistant strength and conditioning coach with the New York Giants from 2007 to 2017.