Snider, who is on Triple-A Las Vegas' seven-day disabled list, was recently sent to the club's Minor League complex in Dunedin, Fla., to continue his rehab.
There is no immediate timetable for when he might be able to return, and there are several obstacles he must overcome before he gets back onto the field.
"He's continuing to receive treatment," manager John Farrell said. "There has really been no advancing of a hitting progression of any kind. The updates that I have [say] that he's continuing to receive treatment to let all the symptoms that he was experiencing when he tried to come back be resolved in its entirety."
Snider sustained the injury while attempting to make a diving catch with the 51s on April 26. He was listed as day to day but eventually had to be placed on the seven-day DL after the wrist failed to improve as expected.
The 24-year-old returned to action on May 9, but the symptoms did not go away. He proceeded to record just one hit in six games before being shut down for a second time.
The club then decided to send Snider to the Bobby Mattick Training Center to continue his rehab.
"[We] felt like it was going to be a seven-day DL situation that would have him back on the field, but when it recurred and there was no clear-cut return date, as we've done with most of our players, [we got him] back to our rehab center in Dunedin," Farrell said.
The injury woes could not have come at a worse time for Snider, who could have been in line for a promotion to the big leagues after left fielder Eric Thames was optioned to Las Vegas.
Thames was instead replaced by fourth outfielder Rajai Davis, and Snider will have to get healthy and regain his stroke at the plate before the Blue Jays contemplate any significant changes to the roster.
Snider is hitting .333 with five home runs and 27 RBIs in 26 games with Las Vegas this season. He is a career .248 hitter over parts of four seasons in the Major Leagues.