In short, No. But there are some mitigating factors that indeed could lead to a squirrel carrying and spreading Parvo. Parvovirus is spread via Stool or Vomit of an effected animal. Now dogs are the primary carrier of parvo but there are a few other animals that can carry the virus. An example would be coyotes and other wild canids such as Wolves, foxes, jackals and dingoes.
Now Squirrels are not Canids, so they cannot carry the virus in the typical sense but they can carry contaminated fecal matter or debris from one yard to another, thus spreading the virus. They often will steal dog food from a bowl and run off with it, if the dog that ate last was infected and another dog get a piece of that kibble the chance for infection is high.
So in short squirrels cannot carry parvovirus in the traditional sense but can spread the virus through other means.
What you need to remember is that Parvo is a super hardy virus that has the ability to live outside of a host for up to a year! That’s right a year! According to Utah Veterinary clinics it can live in extreme heat and frigid cold so be cautious as it can remain in the soil and effected area long after fecal matter or vomit is removed.
Personally I use one of the few cleaners that actually kills parvo Rescue One Vet Strength Cleaner which also comes in Wipes. I highly recommend it and advise that if you do indeed know of an are of contamination that you clean it very thoroughly.