The cover art was noted for Lopez's use of Designer Heidi Lee's Endless Echo Hat that was previously worn by a man known as Di Mondo.
The singer described "Medicine" as a "very sassy song, very kind of woman empowerment".
It marks Lopez's first release under Hitco Entertainment, and her third collaboration with French Montana, following "Same Girl" and "I Luh Ya Papi".
On April 3, 2019, Lopez debuted the song live on The Morning Mash-Up on SiriusXM Hits 1 Celebrity Session.
The song serves as the opening number to Lopez's It's My Party Tour.