It was first recorded by Crudup in Chicago on November 8, 1950, with Ransom Knowling on bass and Judge Riley on drums, and was released as a single on RCA Victor 22-0109.

It gained further exposure in covers by Elvis Presley, who placed his version on the B-side to his 1956 single "I Want You, I Need You, I Love You"; by Wanda Jackson who often shared the same bill as Elvis Presley; by Creedence Clearwater Revival, who recorded it as a track on their 1970 album, Cosmo's Factory; and by John Lennon (incorrectly titled "Since My Baby Left Me"), recorded during the Rock 'n' Roll sessions in 1973, but first released posthumously on Menlove Ave. in 1986. It was included as a bonus track (still incorrectly titled) on the 2004 CD version of Rock 'n' Roll. It was also a # 37 UK Singles Chart hit in 1964 for Dave Berry and the Cruisers. Elton John used a snippet of "My Baby Left Me" as part of a medley (along with a snippet of the Beatles' "Get Back") during his concert performance of "Burn Down the Mission" on his 11-17-70 live album.

"My Baby Left Me" was covered by rock band Slade and released as a single in 1977 as a tribute to Elvis Presley, who died in August of that year. The Slade version merged another Crudup written track, "That's All Right". The single spent four weeks on the UK Singles Chart, peaking at #32. It became Slade's last charting single until their career revival in 1980. The single was rated #788 for 1977 on Rate Your Music.

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