Cano broke his hand Sunday after the team's loss to Detroit and was placed on the 10-day disabled list.
According to The Athletic's Ken Rosenthal, Cano's suspension was pending when the injury happened, and Cano's time on the disabled list will count toward his 80-game suspension.
KIRO reports that before his injury Sunday, Cano was batting .287 with four home runs and 23 RBIs in 39 games.
Cano signed a 10-year, $240 million contract with the Mariners in 2013, after spending the first nine years of his career with the New York Yankees.
The Mariners are currently in third place in the AL West with a 23-17 record entering Tuesday's home game against the Texas Rangers.