A Wagga man has handed himself in to police this morning for allegedly vandalising Gundagai's iconic dog on the tuckerbox.

The 28-year-old was taken into custody at Wagga Police Station and was charged with one count of destroy or damage to property.

The man has been granted conditional bail and is due to face Wagga Local Court on September 11.

A motorist traveling along the side of the Hume Highway, Gundagai, noticed a man vandalising the statue about 4pm on Saturday.

Earlier

Police have released images of people who could assist an investigation into vandalism of the dog on the tuckerbox statue at Gundagai.

Riverina Police District investigators wish to speak with a man and woman in two images released on Monday morning.

The man is described as being of medium build with black hair. He is depicted in the image wearing a black jumper, light tracksuit pants and black glasses.

The woman was described as being of thin build with dark hair.

She was pictured wearing blue jeans, a black top and brown jacket.

Police have been told at about 4pm on Saturday a motorist travelling along the side of the Hume Highway, Gundagai, noticed a man vandalising the statue.

The dog and tuckerbox were dislodged from the base of the statue, falling into the surrounding fountain.

Anyone with information or dashcam footage that may be able to assist investigators are urged to contact Gundagai Police Station on 02 6944 0499 or Crime Stoppers on 1800 333 000.

On Monday morning, Riverina MP and Deputy Prime Minister Michael McCormack condemned the vandalism as "Absolutely disgraceful".

"This is a famous landmark ... real Australia. What's wrong with some people?" he stated on social media.

"Just spoke to (Cootamundra-Gundagai) Mayor Abb McAlister who said the community was upset about what's happened to their dog on the tuckerbox.

"The statue has lost an ear and had his nose damaged in a weekend incident. As Abb put it: 'For the people of Gundagai he's part of your family. He's your mate'."