Byrd, 34, is currently a free agent, and will be placed on the restricted list for the duration of his suspension, which began immediately, AP reported.
He started the season with the Cubs and was dealt to the Red Sox on April 21. He was designated for assignment by Boston on June 9 and released four days later.
He hit .210 in 47 games with the two teams, though he hit .270 with a homer and seven RBIs in 34 games with Boston.
He has played for five teams in 11 major league seasons and is a career .278 hitter.