Turn off the fridge, unplug it and throw everything out. Although it's unlikely that bed bugs will be on the food, it's best to discard everything, including any storage containers, in case the bugs have laid eggs.
Vacuum the inside and outside of the fridge. This will help get rid of most of the bugs and eggs.
Wipe down the fridge using vinegar and washing soda. Vinegar is a known bedbug deterrent.
Put on protective gloves and wipe down the inside and outside of the fridge again, this time using very hot or just-boiled water. Hot water that's around 120 degrees Fahrenheit will kill bed bugs and their eggs; the temperature of boiled water is around 212 degrees Fahrenheit. Dry the refrigerator with a clean towel.
Vacuum the fridge again, to ensure that no bugs or eggs remain; vacuum the coils as well. The fridge should now be bug-free.
Refill the fridge, plug it back in and turn it on.