The all-star reliever is seen sitting on a bench with his legs outstretched wearing a dark shirt and pants.
Police said a professional standards investigation has been launched into the leaked photograph.
Toronto police said Osuna, 23, was charged on Tuesday in relation to an incident that happened overnight.
Authorities did not provide any details on the circumstances of his arrest to protect the identity of the alleged victim.
A police source confirmed to Global News that the arrest happened in the 14 division and that it was a “domestic related” incident.
The source said that police saw “significant injuries” on the alleged victim, who provided a video statement to officers.
It was the concierge at the front desk of the residence who called police, the source added.
Ron Waksman, vice-president of news content for Global News and Corus Radio, told Global News Radio 640 Toronto’s Kelly Cutrara Wednesday afternoon that there has been “a little bit of criticism, more like feedback” in response to the publication of the photo.
However, he said there are good reasons to provide as much information as possible in an effort to get a fuller understanding of what happened.
“When you have a favourite son of a city, a high-profile athlete – somebody young that typically people want to get behind, this sort of an athlete, this sort of a person – and when this kind of a thing happens, there’s disappointment,” Waksman said.
He said justice needs to be transparent and seen to be done.
“There is a very deep cynicism in society today, and we hear it all the time and I’m sure you hear it, that celebrities, and sports figures, and the powerful get special treatment under the law,” Waksman told Cutrara.
“I think this picture makes it pretty clear that the suspect in this case was, at least on the surface, subject to exactly the same judicial process and circumstances as any ordinary citizen would be.”
The Blue Jays closer has since been put on administrative leave by Major League Baseball (MLB).
MLB said in a statement on Tuesday that they take the allegations seriously and are investigating the circumstances of Osuna’s arrest.
VIDEO: Blue Jays pitcher Roberto Osuna charged with assault
The Blue Jays had planned to host a free Roberto Osuna T-shirt promotion at the Rogers Centre on Thursday but that was scrapped to feature infielder Yangervis Solarte instead.
Osuna is scheduled to appear in court on June 18.
— With a file from Kerri Breen