Snell retired his first two batters on popups to left field. He was facing Trea Turner when he suddenly left the mound with a 2-1 count, having thrown 11 pitches. The left-hander limped slightly as he walked off with the groin injury.
Manager Jayce Tingler said after the game that Snell is day to day.
"It's something that he's dealt with in the past," Tingler said. "It usually doesn't come on until the sixth or seventh inning. For whatever reason, today it tightened up on him early. He says he's walking better now. He already feels a little bit better."
It was a significant blow to the Padres, who are fighting for the second NL wild card.
The 2018 AL Cy Young Award winner is 7-6 with a 4.22 ERA. He set a franchise record with 13 consecutive hitless innings across his last two starts.
Snell took a perfect game into the seventh last Tuesday against the Los Angeles Angels before walking two batters and allowing a two-out, two-run single to Jo Adell on his 96th pitch. He struck out 11.
Snell was making his 27th start of the season, tied with Joe Musgrove for most on the staff.
Nabil Crismatt replaced Snell in what suddenly became a bullpen game. The Padres used seven pitchers in the 8-0 loss.