Brenda Millson, of Newscastle, Ont., said she was shocked when she read the letter, which arrived in her mailbox on Friday.
The author of the typed one-page letter claimed to be a mother who lived in the neighbourhood and was upset at the noises Millson's grandson Max made when he was outside.
The letter went on to say the boy's "noise polluting whaling," scared the author's "normal children."
It also included statements such as "he is a hindrance to everyone and will always be that way" and "do the right thing and move or euthanize him."
Millson said she immediately reported the letter to police.
She said Max lives with his parents and older brother in Oshawa, Ont., but he had been visiting her home in Newcastle.
She said the author of the letter may have assumed she is Max's mother.
"At first I couldn't believe what I was reading," she said, adding that she was shaking in disbelief.
"It's just so sick."
Durham regional police said they have been investigating since Friday and that they are taking the letter seriously.
Max's mother, Karla Begley, 44, who is in a wheelchair with multiple sclerosis, said police told her they had never seen a letter "that despicable."
The only hostility the family had sensed in the Newcastle neighbourhood was four years ago, she said.
At the time, Max loved to throw a ball in the backyard and as he often threw it over fences, Millson had written her name and address on it, Begley said.
One day it arrived in the yard tattered, she said.
"They took the time to shred the ball with scissors and throw it back over."
Begley added the family did not know what yard the ball was thrown into.
Millson said Max is a wonderful, sweet and lovable boy with a 16-year-old brother who was "infuriated" and "disgusted" by the letter.
Millson said the letter is "pretty gutless."
On Sunday night, at least 120 people waited outside the home for more than an hour in order show their support, Begley said. Families with autistic children drove in from Oshawa to show their support.
"Max was high-fiving everyone. He didn't understand but knew it was for him," Millson said.
Begley said support for the family following the letter has been "bittersweet," adding it's too bad it took such a letter to bring attention to a special needs child.
"It's just a reminder, you know, you've got to treat these kids like they need to be treated," Begley said. "They just want to belong."