In general, no, a standard Attack of Opportunity (AoO) will not disrupt movement by default.
AoO's do trigger from an enemy taking a move action, or on leaving a square during a move action. So, from your mechanical example, the creature would declare he is taking a Stride action, and the monk could take an Attack of Opportunity immediately, or could wait until the creature left a square which he is able to reach. With a normal AoO, the creature's action would not be disrupted, and he would then continue his movement action as he saw fit. Or, the monk might kill the creature, which would stop it moving further. As another example, if the creature instead announced it was drawing a weapon, this is a Move Action with the Manipulate trait which triggers AoOs and can be disrupted by default. If the monk Critical Hit during an AoO from this trigger, the weapon would not be drawn. If the creature was still alive or had actions left, it could try again.
There are special abilities that change this default behaviour. One example is the feat Impassable Wall Stance where any Critical Hits from Attacks of Opportunity will disrupt triggering movement. Another is Disrupt Prey, which doesn't actually trigger an AoO, but does trigger a Strike that can disrupt movement on a Critical Hit. Stand Still is a Monk feat that also triggers an attack on a move action but isn't an AoO. I couldn't find any more, but there might be others (now or added in the future).
All of these examples say they 'disrupt the triggering action' on a critical hit. They also trigger on leaving a square during a move action, or on the move action itself. With any of the example abilities here, an attacker potentially COULD disrupt the movement action. In these cases, the creature has the action end at the point of triggering, and undoes the triggering movement out of that square. If the creature still has any actions remaining, it could attempt to move again. Given that it is almost impossible to have more than one reaction, the monk would be very unlikely to be able to react again, although other allies might be able to.
So, if the Monk in your example has access to any of these abilities, if the creature declared a Stride, the Monk could attack either when the move was announced or when the creature left a square he could reach. With a Critical Hit, the rest of the move action would be cancelled. Any movement that had already happened before the AoO was triggered would still stand. In this way, the Monk could wait until the creature was in a better position, such as a flank, before striking.
The last little wrinkle to note is that the Step move action specifically doesn't allow any reactions to trigger, but it does use an entire move action to move only 5 feet.