Marshall was born in Bridgetown, Barbados. His father, Denzil DeCoster Edghill, also an outstanding cricketer who played for Kingspark cricket club in St. Philip and the son of Claudine Edghill and Guirdwood Ifill, was a policeman; he died in a traffic accident when Marshall was one year old. His mother was Eleanor 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.