Human, dog, and cat parvovirus are all contained to their own species. Which means they are all separate viruses. So, the answer is no. But, I would have the dog immunized against the virus to protect the dog.
People are not at risk for parvo. Parvo is common in many dogs mainly during the first few months of life. Parvo is most commonly spread by cats and it is a good idea to ensure they are vaccinated to help prevent it.