Right-hander Dennis Santana was recalled from the alternate training site at Glendale, Arizona, to fill the roster spot.
Gonsolin, 26, made the Opening Day roster for the first time but has not pitched this season. He was 2-2 with a 2.31 ERA and 46 strikeouts in eight starts last year for the World Series champions.
"That shoulder inflammation, it's something that's been kind of lingering for the last few days," manager Dave Roberts said. "He went out there and played catch today, didn't feel great, so I think it's more being cautious with Tony being a big part of our club."
Santana, 24, is 2-2 with a 6.66 ERA and 28 strikeouts in parts of four seasons with Los Angeles. He made his major league debut at Coors Field on June 1, 2018.