The four-year-old was in Skegness, Lincolnshire, when a Jack Russell-type dog allegedly bit her a number of times at about 13:45 BST on Saturday.
The owner of the animal allegedly refused to provide her details to the parents of the child.
Police are treating the incident as an offence of having a dog dangerously out of control in a public place.
The dog had allegedly been sitting under the owner's chair at the time and was not on a lead.
The girl required hospital treatment following the incident off Grand Parade.
Dogs are banned from this area from 1 May to 30 September.
A dog attack on a girl on a beach has led to police releasing a picture of the animal's owner.