Crisp will not have his option picked up by the Indians, thus making him a free agent, Paul Hoynes of Cleveland.com reports.
Crisp is not in the lineup for Friday's game against the Royals.
Crisp went 2-for-4 with a two-run home run and two runs scored in the Indians' 7-4 win over the Tigers.
Crisp went 2-for-4 with a double and a three-run homer against the White Sox on Wednesday.
Crisp will DH and bat leadoff Saturday against the Marlins.
Crisp was added to Cleveland's 40-man roster Thursday.
Crisp was traded to the Indians on Wednesday in exchange for minor leaguer Colt Hynes.
Crisp is not in the lineup for Tuesday's matchup against Houston.
Crisp is out of the lineup Wednesday against the Indians.
Crisp is out of the lineup for Saturday's game against the White Sox.