These packets contain silica gel, which is not considered chemically and biologically toxic upon ingestion in most dogs. Stomach upset has been seen in dogs and cats who have accidentally eaten one of these packets. Symptoms include nausea, vomiting and lack of appetite.
There can be additional harmful effects, particularly if the packet was used for medication. Silica acts as a dessicant and can absorb qualities of a medicine when it's in a medicine bottle. For example, if your dog ate a silica gel pack that came out of your heart medication, the silica could absorb the qualities of the heart medication and cause similar adverse effects.
If this came from medication it is very important that your dog see his vet asap. If it was not from medication then you will want to call his vet and see if they want you to bring him in or simply monitor him.