Swanson, who had an MRI in Atlanta on Wednesday, will undergo daily treatment for the remainder of the regular season and will be re-evaluated next week prior to the National League Division Series, which begins Oct. 4.
He left Tuesday's 7-3 victory against the New York Mets with what the team described as left hand soreness. He missed 13 games earlier in the season with left wrist inflammation.
"He swung the bat and something didn't feel right," manager Brian Snitker told reporters Wednesday. "Which is why he'd alarmed me a little bit. He'd been feeling fine, hadn't been complaining about anything.
"... It's your hand. That's a big deal in this game. We'll just have to wait and see."
Swanson, the first overall pick in the 2015 draft, is having a bounce-back season after a disappointing 2017. He is hitting .238 with 14 homers and 59 RBIs.
Charlie Culberson will serve as the shortstop while Swanson is out of the lineup.
"It sounds like it's just something to rest," Snitker told reporters about Swanson's injury. "If you play through it, it's just one of those things you have to play through. So hopefully it's not something more than that."