David Slater says he is the owner of the photo of the grinning black crested macaque that went viral when he posted it online in 2011, and is threatening to sue Wikimedia for lost earnings of up to $30,000 (22,500 euros).
But the not-for-profit foundation, which oversees Wikipedia among other online resources, refuses to remove the picture from its bank of royalty-free photographs.
"Under US laws, the copyright cannot be owned by a non-human," Wikimedia spokeswomen Katherine Maher told AFP.
"It doesn't belong to the monkey, but it doesn't belong to the photographer either," she added.
Slater was with a party of Dutch researchers on a small group of Indonesian islands when the curious primates began rummaging through his possessions.
He described how one snatched his camera and began pressing the shutter button, in the process taking a perfectly composed selfie.
Slater argues that Wikimedia's defence is based on a technicality, and that there is "a lot more to copyright than who pushes the trigger on the camera".
"I own the photo but because the monkey pressed the trigger and took the photo, they're claiming that the monkey owns the copyright," he said.
The dispute came to light on Wednesday when Wikimedia published its transparency report, which revealed that it granted none of the 304 requests to remove or alter content on its platforms over the
last two years.