Rauch hurt her knee in training, Voss-Tecklenburg said, and while the coach did not give the specifics of the injury, she said "Feli cannot play, but we are happy that the diagnosis isn't worse than what she has.
"We did have a diagnosis quite quickly, which was relatively positive and has given us a bit of breathing space," the coach said.
The second-ranked Germans thrashed Morocco 6-0 in their opening game, the most lopsided match so far in the tournament. Colombia opened their campaign with a 2-0 win over South Korea.
The Germans were already missing defender Giulia Gwinn, who played a key role in her team's second-place finish to England at the 2022 Euros, and Bayern Munich defender Carolin Simon, who ruptured her ACL in a friendly versus Zambia earlier this month in their final game before the World Cup.
"(Rauch) is the third defender that we lose," Voss-Tecklenburg said. "We know what type of backup options we have. We always know we want to stick together as a community and really take these challenges on and we will do that as a team and we will be prepared for that."
Voss-Tecklenburg, who was appointed Germany's coach in 2019 after six years with Switzerland, believes her team can grow from the challenge.
"We take some strength from that. And we want to basically be in that mindset where it doesn't matter who's standing there on the actual pitch," she said. "We are going to work together, we're going to help each other out. We trust in all our players and therefore we will be able to compensate for this injury."
Injuries have become a theme of the Women's World Cup, with many top players sidelined in the build-up and several more since the tournament kicked off. Haiti's Jennifer Limage tore her ACL on opening night versus Australia, while the Matildas were missing leading scorer Sam Kerr through their first two games (calf injury).
England midfielder Keira Walsh suffered what appeared to be a serious knee injury on Friday against Denmark. The FA has not released details yet on the severity of the injury.
"We actually talked about this when we were driving here, soccer is a risky type of sport. We have players who are injured here. We try to take preventive measures. But it is a contact sport and of course injuries are part of it," Voss-Tecklenburg said.
"There might be players who will not be able to finish this tournament. We want to play against the best and we want to offer our players the opportunity to have positive experiences and to go through the tournament being able to play. If that isn't the case, then yes, it does touch us. Yes, injuries hurt us. But that's not only the case for our team."
Germany play South Korea in their final Group H game on Aug. 3.
