A humble reference, for your viewing pleasure
Assuming you want both parties to be human, the prey to remain intact, and with minimal stretching on the part of the predator, this is pretty much the minimum difference you might expect.
The smallest bit the prey has to go through is the esophagus, which for the average (~5′9″ tall) human is pretty roughly between 1.5 and 2 cm (but can stretch up to about 3 cm) in diameter. Assuming the prey goes down vertically, the biggest bit the predator has to fit throat-ways is the shoulder, and the average human shoulder width is about a foot and a half, or ~46 cm.
This means that prey needs to be about 6.5% the size of the predator, or conversely that the predator needs to be about 1,524% the size of the prey. For the 5′9″ human, that means the prey would be about 4.5 inches tall, or that the predator would be about 87 feet tall.
For comparison, this means that the smaller party will be about a third again the height of a credit card, or 75% the height of an iPhone:
and that the larger party will be comparable to a 10-story building, or a blue whale
Wolfram|Alpha is nice for getting more comparisons by length and height.
Of course, this is just a reference, and an approximate one at that; I tried to keep the post numbers to two sig figs.