In the film, Groot is a heroic extraterrestrial tree-like creature who only says three words: "I am Groot", but he uses different intonations to convey his meaning.
Writing on Facebook, dad Josh Dunlap said: "My son began to mimic [Groot] and he would use the word 'bah' for a lot, but after he saw the film, he would change the tone in which he said it to convey a different meaning."
Gunn shared the touching message on his own Facebook page and wrote: "I love making movies because of stories like this. Thank you."
In the original message to Gunn, Dunlap wrote: "My son Sawyer is four years old and has a condition known as dyspraxia, which not only interferes with motor skills but speech as well.
"When Guardians came out, he could only say about three words and would communicate to his mother and I by other means.
"When he saw Groot, something clicked inside him and he connected with him on a level I haven't seen."
The dad continued: "He would also start saying Groot for many things as well. Since that, he was finally able to go to a speech class and it has helped amazingly.
"I just wanted to thank you though, for a script and movie that was written so well that a four-year-old, three at that time, could connect with someone who had the same language barrier."
Dunlap was taken by surprise when his post was shared by the director.
The dad wrote: "My wife and I are in complete shock right now... never expected James Gunn to even see the post let alone reply. Thanks everyone for your kind words. Wow."
To which Gunn replied: "I have many friends who get a lot of negative messages online - I'm very grateful for the huge, vast majority of positive and kind people who follow me.
"I get to hear stories like this, and then read all the amazing comments below. Truly wonderful."
When the post started to gain attention, another mum expressed her child's connection to the character, too.
She said: "Thanks so much for sharing this and thanks to Josh for sharing too. My son has dysarthria and it causes similar speech issues as dyspraxia. He's always felt a connection with Groot for the same reasons."