He is hitting .224 with five home runs and 21 RBIs in 49 games this season.
"I tried to do as much as I could to avoid [the DL]," Snyder said. "I missed some games and it pretty much got to a point where I was wasting a spot on the bench, and it wasn't going to be something where I could heal it in a couple of days."
In a corresponding move, the D-backs promoted catcher Luke Carlin from Triple-A Reno.
"That's the one position on the field where you can't play short," D-backs manager A.J. Hinch said. "[Ryan] Roberts can catch in an emergency, but the way [Snyder] was moving around in Seattle, it made it a smart move to go ahead and make a catching move."
Carlin hit .287 with four home runs and 22 RBIs for the Aces.
"He was with us in Spring Training and he was doing a good job in Triple-A," Hinch said. "He takes great pride in handling a pitching staff. He'll be a true backup for us. [Miguel Montero] will be the starter, but I'll work him in and give him some time."
Snyder joins pitchers Brandon Webb (shoulder) and Tom Gordon (hamstring), along with infielders Chad Tracy (oblique) and Conor Jackson (general illness) on the disabled list. Jackson was transferred to the 60-day disabled list Tuesday to make room for Carlin on the 40-man roster.
Before Tuesday's game, Hinch replaced center fielder Chris Young in the lineup with Gerardo Parra due to a groin strain.
"We've been dealt a few blows but a lot of teams have," Hinch said. "Other teams have been dealing with the injury bug, dealing with winning streaks and losing streaks and things like that. We are not going to use it as an excuse."
Jesse Sanchez is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.