Byrd played for the Chicago Cubs and Boston this season. He hit .210 with nine RBI and one home run in 47 games with the two clubs.
He will be placed on the restricted list while on suspension, which began immediately.
Byrd, 34, previously played for Philadelphia, Washington and Texas. He was a 2010 all-star and has a .278 career batting average with 445 RBI and 82 homers.
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