I know that infestation movement does not provoke opportunity attacks. However, I have a different question:
The description of booming blade (SCAG p. 142) states:
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails. On a hit, the target suffers the attack’s normal effects, and it becomes sheathed in booming energy until the start of your next turn. If the target willingly moves before then, it immediately takes 1d8 thunder damage, and the spell ends.
And infestation (XGtE p. 158) says:
You cause a cloud of mites, fleas, and other parasites to appear momentarily on one creature you can see within range. The target must succeed on a Constitution saving throw, or it takes 1d6 poison damage and moves 5 feet in a random direction if it can move and its speed is at least 5 feet. Roll a d4 for the direction: 1, north; 2, south; 3, east; or 4, west. This movement doesn’t provoke opportunity attacks, and if the direction rolled is blocked, the target doesn’t move.