Ramírez was one of the only bright spots for the team's inconsistent offense. The 29-year-old batted .266 with 36 homers, 103 RBIs and 27 steals in the final year of a team-friendly $26 million, four-year deal.
The Indians, who will be known as the Guardians next season, also declined a $7 million option for catcher Roberto Pérez, who gets a $450,000 buyout, and hired Chris Valaika as their hitting coach.
It's possible the Indians, who will transition to Guardians later this month, will look to sign Ramírez to a long-term extension this winter.
"I would really like to stay," Ramírez said after Cleveland finished 80-82 for the club's first losing season since 2012. "But there's no rush. I would really like to stay here the rest of my career. But we have to wait to see what happens. I would love to see what they have to offer."
The 32-year-old Pérez was slowed again by injuries this year. He batted .149 in 44 games in his eighth season with Cleveland.
Ramírez and Pérez were the only position players left from Cleveland's 2016 pennant-winning team, which lost the World Series in seven games.