The Mariners are getting outfielder Xavier Avery in return for Morse.
Morse, 31, is batting .226 with 13 home runs and 27 RBI in 76 games this season.
Morse started the season on fire, hitting six home runs in the season's first two weeks, but was showed by a finger injury and a quad injury that landed him on the disabled list for more than a month.
Morse, since coming off the disabled list on July 29, is hitting .158/.200/.289 in 80 plate appearances. He is making $6.75 million this season in the final year of a two-year deal.
Baltimore starts this weekend's series against the New York Yankees 6.5 games back in the American League East and 3.5 games for the second wild-card slot.