The move was made retroactive to Friday. The Padres recalled right-hander Nabil Crismatt from Triple-A El Paso in a corresponding move.
Snell was placed on the injured list Friday with gastroenteritis, retroactive to July 6.
The Padres also are without right-hander starting pitcher Dinelson Lamet, who is on the injured list with forearm inflammation, and saw Sunday's starting pitcher, Ryan Weathers, exit in the top of the third inning against the Colorado Rockies after suffering an apparent right leg injury while trying to make a play by the first-base line.
Darvish pitched only three innings in his last start, on Thursday against the Washington Nationals, giving up six runs on eight hits. The Padres rallied from an 8-0 deficit in that game to prevail 9-8.
Padres manager Jayce Tingler had announced on Friday that Darvish wouldn't pitch in the All-Star Game, citing back tightness at that time.
The Padres acquired Darvish and Snell in separate blockbuster trades during the offseason. Darvish is 7-3 with a 3.09 ERA and 125 strikeouts this season, while Snell is 3-3 with a 4.99 ERA and 93 strikeouts.