Thank you for your question. My name is***** I have been a small animal veterinarian for 13 years and I'd like to help with your question.
It is always distressing when your dog eats something he shouldn't. There are really two things to be worried about when this happens... First, is it potenially toxic and second, could it cause a blockage.
As for any risk of toxicity, they are not toxic. However, they are also not digestible either. They will not break down and therefore could post some risk of a blockage. In a large dog with something as flexible as a dryer sheet they will usually pass with no problem. In a smaller dog with a smaller intestine it could get bunched up and cause a problem.
Dryer sheets don't show up on an X-rays so there is little you can do to know what is going on in there. I would recommend feeding a high fiber diet for a few days to encourage good intestinal motility and monitor his bowel movements to see if he passes it. You can get a special high fiber diet from your veterinarian or you can try adding fiber to their regular diet with some canned pumpkin or high fiber bread. If he has any vomiting at all, I would take him to a veterinarian. Vomiting is the first sign of a blockage.
You didn't mention how big he is, but if he is a large dog I don't think he'll have any problems, just watch him.
I hope that helps, but if you have additional questions please let me know. If not, please rate my answer.