Marshall was born in Bridgetown, Barbados. His father, Denzil DeCoster Edghill was also an outstanding cricketer who played for Kingspark cricket club in St. Philip the son of Claudine (née Edghill) and Guirdwood Ifill, was a policeman; he died in a traffic accident when Marshall was one year old. His mother was Eleanor (née Welch). Malcolm had three half-brothers and three half-sisters. He grew up in the parish of Saint Michael, Barbados and was educated at St Giles Boys' School from 1963 to 1969 and then at Parkinson Comprehensive from 1969 to 1973.

He was partly taught cricket by his grandfather, who helped to bring him up after his father's death. He played cricket for the Banks Brewery team from 1976. His first representative match was a 40-over affair for West Indies Young Cricketers against their English equivalents at Pointe-à-Pierre, Trinidad and Tobago in August 1976. He made nought and his eight overs disappeared for 53 runs.

Marshall's initial senior appearance was a Geddes Grant/Harrison Line Trophy (List A) match for Barbados on 13 February 1978; again he made a duck and did not take a wicket. Four days later, he made his first-class debut against Jamaica, and whilst he failed to score runs, he claimed 6–77 in the Jamaican first innings. On the back of this single first-class appearance he was selected to tour India in 1978/79, many first-choice West Indian stars being unavailable having committed themselves to playing World Series Cricket. Marshall heard of his selection on the radio while working in the storeroom at Banks Brewery and later claimed he did not know where India was.

Marshall made his Test début in the Second Test at Bangalore on 15 December 1978. He immediately developed a career-long antipathy to Dilip Vengsarkar due to his aggressive appealing. Despite doing little of note in the three Tests he played on that tour, he did take 37 wickets in all first-class games, and Hampshire saw enough in him to take him on as their overseas player for 1979, remaining with the county until 1993. He was in West Indies' World Cup squad, but did not play a match in the tournament. Hampshire were not doing well at the time, but nevertheless he took 47 first-class wickets, as well as picking up 5–13 against Glamorgan in the John Player League.

Marshall came to prominence in 1980, when in the third Test at Old Trafford he accounted for Mike Gatting, Brian Rose and Peter Willey in short order to spark an England collapse, although the match was eventually drawn despite Marshall taking 7–24. After 1980/81 he was out of the Test side for two years, but an excellent 1982 seas