Snider, who is currently on the seven-day disabled list for Triple-A Las Vegas, hadn't played in an official game since May 17.
The 24-year-old had been working out at extended spring training, where on Wednesday he went 2-for-4 in an exhibition game. He is now taking the next step and appears to be on the way to a full recovery.
"He's felt no ill effects of the wrist," Blue Jays manager John Farrell said. "He'll now join Dunedin for the remainder of this week and get at-bats there before either the next move is made, wherever that is, whether it's a return to Vegas or wherever that might be.
"But the most important thing is he's got no issues going on, he's swinging the bat well and [it's] very encouraging."
Toronto closer Sergio Santos is also easing his way back. Santos has been out since April 21 with inflammation in his right shoulder, but he threw off a mound on Wednesday for the third time since suffering the injury in Kansas City.
"It will be determined whether he takes live BP his next outing or needs to get back onto the mound without hitters," Farrell said. "But it has been fastball-changeup, 25-30 pitches per bullpen, increasing intensity with each one. We're moving along the program. "
Santos has yet to resume throwing a slider, which is arguably his best pitch. The Blue Jays won't initiate that part of the program until more arm strength has been built up.