It depends on what triggered the shift.
As @ioanwigmore pointed out, PHB1 p.287 describes a
Charge as (emphasis mine):
Move and Attack: Move your speed as part of a charge and make a melee basic attack or a bull rush at the end of your move.
As @Ravn pointed out, PHB1 pg 268 describes an
Immediate Interrupt as (emphasis mine):
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.
If the attack was the trigger (for example,
Trigger: You are the target of a melee attack.), then movement is already done. The charger has already transitioned from the "movement" phase of the charge to the "attack" phase, and can't move any more.
If the movement was the trigger (for example,
Trigger: A foe enters a square adjacent to you.) then the shift happens before the "movement" phase of the charge resolves (i.e. finishes). In that case the charger can continue as long as they have movement left and each square of movement brings them closer to the target's new location.
The pseudo-momentum doesn't say you can't change directions, only that you must always be getting closer to your target. For example, because of how 4e counts diagonals, the following 90 degree turn in mid-charge is perfectly valid:
o = empty space,
X = obstacles,
T = target,
S = charger's starting position,
F = charger's final position,
P = charger's path