The 20-year-old Denmark international returned to match action in the first leg of the tie after a five-month spell on the sidelines, but complained about pain in the same hamstring after the final whistle against the Red Devils.
Boilesen consequently missed last weekend's 4-1 Eredivisie win over NEC, and a scan has now revealed that the left-back will be out of action for three weeks due to the ailment, ANP reports.
Ajax are already without first-team regulars Gregory van der Wiel, Eyong Enoh, Derk Boerrigter and Kolbeinn Sigthorsson for the match at Old Trafford due to injury, while Theo Janssen and Dmitry Bulykin are both doubtful.
The Amsterdam side were beaten 2-0 at the Amsterdam ArenA last week, and need to score at least three goals on Thursday if they are to reach the last 16.
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.