The 37-year-old was detained following a joint investigation between Lancashire Police and the RSPCA.
A member of the public filmed the dog being punched at about 15:15 GMT on 10 December in Hendon Road, Nelson.
The RSPCA said the dog - an adult female Staffordshire Bull Terrier cross - has been checked over by a vet and is now in the charity's care.
RSPCA Inspector Charlotte Booker thanked people for their response to an appeal and said: "It has been absolutely huge over the last 48 hours and we are very grateful for the scale and quality of this response.
"The same name came forward various times so we were able to verify information quickly. I'd also like to thank Lancashire Police for their help in this joint operation."
A man has been arrested on suspicion of animal cruelty after a dog was attacked on a Lancashire street.