Shrewsbury have also beaten second strings from Wrexham and Chester on the cup run. They beat Chester 2-1 in September, with Kevin Street on the scoresheet again.
They then saw of Wrexham 1-0, with Street again the scorer. The former Crewe man has scored in every round so far.
In previous meetings this year, Town's reserves have gone down 5-2 and 3-0 to the Man Utd side, and this will be a tricky tie. United are top of the Division One West, with only two defeats all season.
The game is set for a 7pm kick off on April 11.