The family of the youngster posted on social media that he needed 30 stitches after the incident which is understood to have taken place in the vicinity of Hillhead Road around 2.30pm on January 12.
They launched an online appeal yesterday (Wednesday, January 15).
The post on a community Facebook page read: “My grandson Kody was attacked by a big black dog.
“Kody has had surgery and has over 30 stitches in his face.
“THIS DOG has to be found before some child is hurt again”.
A police spokesperson told the Herald today (Thursday, January 16): “Police have been made aware of an incident in which a young boy was injured after an attack by a dog in Kirkintilloch on Sunday, January 12.”