Born in Detroit, Michigan, he grew up in the northern suburb of Berkley. He graduated from Berkley High School in June 1971.

He began playing guitar at age ten. During and after High School he led the band Astigfa (an acronym for "a splendid time is guaranteed for all", a lyric from The Beatles' "Being For The Benefit of Mr. Kite"). He got his first break in 1978, playing John Lennon in the musical Beatlemania, first as an understudy in New York, then in the West Coast company, then in a national touring company. He left the show in February, 1980.

After launching a trio in New York (with his brother Robert on drums, and Chris Donato on bass), he recorded "Something's Gonna Happen", for Alan Betrock's Shake Records, after which he was signed to Warner Bros. Records. Robert Gordon took Crenshaw's "Someday, Someway" to #76 in 1981, and Crenshaw's own version made #36 the next year; it would be his only solo Billboard Top 40 'Pop' hit. On the Cash Box magazine chart the song fared slightly better, reaching #31. Its biggest reception was at AOR (Album Oriented Rock) radio, reaching #25 on Billboard's Rock Tracks chart. The song, "Til I Hear It from You", sung by the Gin Blossoms and co-written by Crenshaw, reached #11 on the U.S. Billboard Hot 100 chart in 1996.

Crenshaw's eponymous first album included the U.S. hit, Someday, Someway. His second album, Field Day, released in June 1983, sported a somewhat heavier sound, as evidenced on "Whenever You're On My Mind," that reportedly displeased a few listeners, but which is regarded by many critics as Crenshaw's best, and one of the classic power pop statements, although Crenshaw's work, somewhat like the late Alex Chilton's, transcends the genre. "Some of the stuff I've done you could call power pop," he told an interviewer, "but the term does have sort of a dodgy connotation." Although the song did not reach the Top 40 on Billboard's Pop Charts, "Whenever You're On My Mind" reached # 23 on Billboard's Rock Tracks chart.

In 1989, he compiled a collection of Capitol Records country performers of the 1950s and '60s called Hillbilly Music...Thank God, Vol. 1, which was extremely well received. In 1993, he made an appearance in the cult TV show The Adventures of Pete and Pete, in the role of a guitar-playing meter reader, and in 1994, he published a book, Hollywood Rock: A Guide to Rock 'n' Roll in the Movies.

He continued to record in the 1990s and 2000s. "Better Back Off", a song from the album "Life's Too Short," reached # 17 on Billboard's Alternative Songs Chart. In 1999, Crenshaw released the critically acclaimed #447. In the 2000s, he played guitar as a special guest with the reunited members of the MC5. Crenshaw continued to perform at about 40-50 concerts a year, most of them within driving distance of his family home. Crenshaw himself has dubbed these shows part of “the NPR singer-songwriter circuit.”

Crenshaw penned the title track from the 2007 film Walk Hard starring John C. Reilly; the song, as sung by Reilly, was nominated for a Golden Globe Award for Best Original Song.

Jaggedland, was released in June 2009 on his new record label 429 Records. In 2011, Crenshaw began hosting a radio show called The Bottomless Pit on WFUV in New York, featuring his vast collection of recorded music.

His music has roots in classic soul music and Buddy Holly—the latter to whom Crenshaw was often compared in the early days of his career, and whom he portrayed in the 1987 film La Bamba. Crenshaw is also a noted Guitarist. A quote from Trouser Press summed up Marshall Crenshaw’s early career: “Although he was seen as a latter-day Buddy Holly at the outset, he soon proved too talented and original to be anyone but himself.” AllMusic Guide described Crenshaw’s style: “He writes songs that are melodic, hooky and emotionally true, and he sings and plays them with an honesty and force that still finds room for humor without venom.”

On October 23, 2015 Crenshaw played at the Adler Theater in Davenport, Iowa, at a campaign event for Bernie Sanders, Democratic candidate for President, which also featured Wayne Kramer and numerous other performers.