Manne's father and uncles were drummers. In his youth he admired many of the leading swing drummers of the day, especially Jo Jones and Dave Tough. Billy Gladstone, a colleague of Manne's father and the most admired percussionist on the New York theatrical scene, offered the teenage Shelly tips and encouragement. From that time, Manne rapidly developed his style in the clubs of 52nd Street in New York in the late 1930s and 1940s. His first professional job with a known big band was with the Bobby Byrne Orchestra in 1940. In those years, as he became known, he recorded with jazz stars like Coleman Hawkins, Charlie Shavers, and Don Byas. He also worked with a number of musicians mainly associated with Duke Ellington, like Johnny Hodges, Harry Carney, Lawrence Brown, and Rex Stewart.

In 1943, Manne married a Rockette named Florence Butterfield (known affectionately to family and friends as "Flip"). The marriage would last 41 years, until the end of Manne's life.

When the bebop movement began to change jazz in the 1940s, Manne loved it and adapted to the style rapidly, performing with Dizzy Gillespie and Charlie Parker. Around this time he also worked with rising stars like Flip Phillips, Charlie Ventura, Lennie Tristano, and Lee Konitz.

Manne rose to stardom when he became part of the working bands of Woody Herman and, especially, Stan Kenton in the late 1940s and early 1950s, winning awards and developing a following at a time when jazz was the most popular music in the United States. Joining the hard-swinging Herman outfit allowed Manne to play the bebop he loved. The controversial Kenton band, on the other hand, with its "progressive jazz", presented obstacles, and many of the complex, overwrought arrangements made it harder to swing. But Manne appreciated the musical freedom that Kenton gave him and saw it as an opportunity to experiment along with what was still a highly innovative band. He rose to the challenge, finding new colors and rhythms, and developing his ability to provide support in a variety of musical situations.

In the early 1950s, Manne left New York and settled permanently on a ranch in an outlying part of Los Angeles, where he and his wife raised horses. From this point on, he played an important role in the West Coast school of jazz, performing on the Los Angeles jazz scene with Shorty Rogers, Hampton Hawes, Red Mitchell, Art Pepper, Russ Freeman, Frank Rosolino, Chet Baker, Leroy Vinnegar, Pete Jolly, Howard McGhee, Bob Gordon, Conte Candoli, Sonny Criss, and numerous others. Many of his recordings around this time were for Lester Koenig's Contemporary Records, where for a period Manne had a contract as an "exclusive" artist (meaning that he could not record for other labels without permission).

Manne led a number of small groups that recorded under his name and leadership. One consisting of Manne on drums, trumpeter Joe Gordon, saxophonist Richie Kamuca, bassist Monty Budwig, and pianist Victor Feldman performed for three days in 1959 at the famous Black Hawk club in San Francisco. Their music was recorded on the spot, and four LPs were issued. Highly regarded as an innovative example of a "live" jazz recording, the Black Hawk sessions were reissued on CD in augmented form years later.

Manne is often associated with the frequently criticized West Coast school of jazz. He has been considered "the quintessential" drummer in what was seen as a West Coast movement, though Manne himself did not care to be so pigeonholed. In the 1950s, much of what he did could be seen as in the West Coast style: performing in tightly arranged compositions in what was a cool style, as in his 1953 album named The West Coast Sound, for which he commissioned several original compositions. Some of West Coast jazz was experimental, avant-garde music several years before the more mainstream avant-garde playing of Cecil Taylor and Ornette Coleman (Manne also recorded with Coleman in 1959); a good deal of Manne's work with Jimmy Giuffre was of this kind. Critics would condemn much of this music as overly cerebral.

Another side of West Coast jazz that also came under critical fire was music in a lighter style, intended for popular consumption. Manne made contributions here too. Best known is the series of albums he recorded with pianist André Previn and with members of his groups, based on music from popular Broadway shows, movies, and television programs. (The first and most famous of these was the one based on My Fair Lady, recorded by Previn, Manne, and bassist Leroy Vinnegar in 1956. See My Fair Lady (album).) The music—with each album devoted to a single show—was improvised in the manner of jazz, but always in a light, immediately appealing style aimed at popular taste, which did not always go over well with aficionados of "serious" jazz music, which may be one reason why Manne has been frequently overlooked in accounts of major jazz drummers of the 20th century. Much of the music produced on the West Coast in those years, as Robert Gordon concedes, was in fact imitative and "lacked the fire and intensity associated with the best jazz performances". But Gordon also points out that there is a level of musical sophistication, as well as an intensity and "swing", in the music recorded by Manne with Previn and Vinnegar (and later Red Mitchell) that is missing in the many lackluster albums of this type produced by others in that period.

West Coast jazz, in any case, represented only a small part of Manne's playing. In Los Angeles and occasionally returning to New York and elsewhere, Manne recorded with musicians of all schools and styles, ranging from those of the swing era through bebop to later developments in modern jazz, including hard bop, usually seen as the antithesis to the cool jazz frequently associated with West Coast playing.

From the 78-rpm recordings of the 1940s to the LPs of the 1950s and later, to the hundreds of film soundtracks he appeared on, Manne's recorded output was enormous and often hard to pin down. According to the jazz writer Leonard Feather, Manne's drumming had been heard on well "over a thousand LPs"—a statement that Feather made in 1960, when Manne had not reached even the midpoint of his 45-year-long career.