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The Briton suffered a tear to his oblique muscle during his fourth round encounter with the Spaniard, forcing him to bring the match to a premature end in the second set.
While Alcaraz went on to win the tournament and reclaim his position as world number one, Draper is now set for a spell on the sidelines.
The 21-year-old has decided to withdraw from Miami, in order to focus on making a full recovery rather than risk aggravating the issue.
The world number 43 struggled for fitness during the 2021 season, but played 22 events last year and reached the quarter-finals of the Canadian Open.
Alcaraz won his first ATP Masters 1000 title in Miami last year by beating Casper Ruud in the final.
After being awarded a bye into the second round, he will face either Facundo Bagnis or a qualifier and could take on Andy Murray in round three as he eyes a Sunshine Double.
