I am grabbing this reference from the PHB1 (page 268):
Interrupt: An immediate interrupt lets you jump in when a certain trigger condition arises, acting before the trigger resolves. If an interrupt invalidates a triggering action, that action is lost. For example, an enemy makes a melee attack against you, but you use a power that lets you shift away as an immediate interrupt. If your enemy can no longer reach you, the enemy’s attack action is lost.
From the above I would surmise that if the trap's effect said that the target is slowed or immobilized (on a hit) than it would stop the movement, else you'd take the damage and then continue on as damage alone wouldn't negate the rest of your movement.