It was introduced by Mary Martin and Kenny Baker in the Broadway musical One Touch of Venus (1943). The 1944 hit single was by Guy Lombardo and his orchestra, with vocal by Billy Leach. Barbra Streisand recorded a David Foster arrangement of "Speak Low" for her album Back to Broadway (1993).
The tune is a jazz standard that has been widely recorded, both by vocal artists from Billie Holiday and Tony Bennett to The Miracles and Dee Dee Bridgewater, and such instrumentalists as Chet Baker Gerry Mulligan, Bill Evans, Sonny Clark with Donald Byrd and John Coltrane, Roy Hargrove, Woody Shaw, Bobby Shew, Eumir Deodato and Brian Bromberg. Ella Fitzgerald and Joe Pass recorded this in 1983 (on CD Speak Love). Al Caiola's 1961 version reached #105 on Cashbox magazine's "Looking Ahead" survey. Kurt Weill himself also recorded the song.
"Speak Low" is featured in the 2014 German film Phoenix.