Tatis went down with the injury in the bottom of the third inning during the game at Petco Park in San Diego, during an at-bat when the score was tied 1-1.
Giants starting pitcher Anthony DeSclafani quickly earned an 0-2 lead in the count before Tatis fouled off a pitch and took two balls to even the count. DeSclafani then tossed in an 84.3-mph knuckle curve.
Tatis took a huge hack at the off-speed offering, swinging way before the pitch arrived. He collapsed to the ground and appeared to be in significant pain. A Padres trainer and manager Jayce Tingler took him into the clubhouse. He did not return.
The Padres called the injury a "subluxation," or partial dislocation. Tatis will get an MRI and be re-evaluated Tuesday.
Tatis went 0 for 2 with a strikeout in Monday's 3-2 loss. Darin Ruf, Evan Longoria and Mike Yastrzemski each homered for the Giants in the victory.
The 22-year-old Tatis also injured his left shoulder during a spring training game in March and had been receiving daily treatment for it since. Tingler also said Tatis has sustained previous minor shoulder dislocations.
"That's the same [shoulder]," Tingler told reporters. "It comes out and comes back in. He has been dealing with that. [Monday night] was the first time we've seen it in game action from swinging or anything like that."
Tatis is hitting .188 with a home run and an RBI in four games this season. He leads the National League with 19 plate appearances. The shortstop hit .277 with 17 home runs and 45 RBIs in 59 games last season and signed a 14-year $340 million contact in February.
The Padres next face the Giants in the second game of the three-game series at 7:10 p.m. PDT Tuesday in San Diego. Ha-Seong Kim replaced Tatis in Monday's game and could fill in for the Padres' starting shortstop until he returns from his injury.