Posting under the name Coffeeandtrout, he wrote: "My parents' wedding day, February 1961. I think my dad looks like Matt Damon."
He said the picture was taken in "suburban Seattle" and that they remained happily married until his mother passed away last year.
"Dad's still trying to adjust. They were great together," he added.
The picture sent some people into a frenzy who were convinced that it really was Matt Damon, who is married to Luciana Barroso, or that it had been posted by the actor himself.
Duderds wrote: "The DNA test results are in... you are the Matt Damon!"
Throwingfurtheraway_ wrote: "Are... are you Matt Damon?" Hedgehogknight added: "He's f*****g Matt Damon!"
But he insisted that it would be impossible for either himself or his father to be the actor because they are both older than Matt, who is 45.
He said his father was six foot on his wedding day but that now he is five foot 11 - taller than the actor, who is believed to be five foot ten.
He said his father is "as close as you could get, at least as a dad".
"There's no way you are ugly with those parents," wrote Rapturecity113.
One person, ForkedUpChef compared his mother to Elizabeth Taylor, adding: "Sure hope you scored those genes."
But responding to compliments about his parents' looks, he said he "ruined those genes with tobacco, alcohol, weed and flyfishing".