The 70-year-old was arrested in the early hours of August 18 after a member of the public reported someone driving erratically, The Washington Post says.
Wilson was arrested in Georgia, where The Walking Dead is filmed.
After being pulled over, he reportedly asked to do yoga poses instead of a field sobriety test and admitted drinking scotch and wine.
Wilson appears in The Walking Dead as Hershel, a recovering alcoholic and the owner of the farm inhabited by a group of survivors.
The Walking Dead's network AMC has not yet commented on his arrest.