The 40-second clip, which was filmed at the Cleveland Centre in Middlesbrough, shows Santa trying to talk to the child, but initially, she doesn't seem to be paying attention.
The girl's mum, who is not visible in the film, tells him, 'Sorry, she can't talk very well.'
'Can she sign at all?' Santa asks.
'Yeah, she does animals and things like that,' mum replies - so Santa turns to the girl and begins to communicate with her through sign language.
Instantly, the girl's face lights up, and the pair begin to have what appears to be an in-depth discussion about what she'd like for Christmas.
Watch the touching moment in full
Commenters who can use sign language have been trying to decipher the whole conversation; 'I only think I understand the beginning where he asks her if she wants him to bring her a doll, the rest I'm not sure of yet but I'll keep looking,' one says.
Others are simply watching it for the joy of seeing this little Christmas miracle. 'So sweet, wonderful of him to make a connection with her.. what a great guy and what a precious girl! :)' one typed, whilst another added, 'This guy deserves a medal. Best video I have seen in long time. He made that little girl's year right there.'
A spokesman for the Cleveland Centre told the Gazette: 'We believe the Cleveland Centre Santa is real and this truly shows the magic and spirit of Christmas, just like Miracle on 34th Street.'
'Santa wants to make sure every child who visits really does experience what this time of year is all about. Santa will take his time with each and every child and will try and put a smile on their faces.'
Ever met a Santa that's gone above and beyond for a child? Leave us a comment and let us know your stories!