Tatis hurt his shoulder on Monday when he took a strong swing at a pitch and missed. The Padres called the injury a "subluxation," or partial dislocation, of his left shoulder.
The team re-evaluated Tatis and placed him on the 10-day injured list Tuesday. An MRI showed he also has a partial tear of his labrum.
Padres manager Jayce Tingler and general manager A.J. Preller spoke to reporters Tuesday, but did not provide an exact timeline for Tatis' return.
"Let's be real," Tingler told reporters. "You're not going to replace him. Now, can a group of eight, nine, 10, 11 guys step their game up a small percentage? Can we come together and pull for one another?
"Like I said, you're not going to replace him, but we believe in our guys."
Tatis has had previous shoulder dislocations, but Preller said the Padres don't feel they're putting him at risk by returning him to the field later this season.
"There's always a chance that he can have another episode, another incident, where there's another subluxation," Preller told reporters. "At that point in time, we'll evaluate from there.
"This is not a situation where our doctors, knowing the player, seeing him and examining him, looking at images, feel like we're putting him at issue of, long term, having more damage if he goes out and plays."
Tatis will rehab and rest the shoulder over the next two weeks and be re-evaluated. Preller said he expects the team to treat the shoulder without surgery "right now," but indicated Tatis could go under the knife next off-season.
Ha-Seong Kim started at shortstop for San Diego on Tuesday. The Padres also could use Jorge Mateo, Jake Cronenworth and third baseman Manny Machado at the position in Tatis' absence.
Tatis, 22, is hitting .167 with a home run and an RBI in five games this season. He signed a 14-year, $340 million contract extension in February.
The Padres (4-2) next host the San Francisco Giants (2-3) at 1:10 p.m. PDT Wednesday at Petco Park.