Gomez underwent a scan on Sunday that showed the striker suffered a torn thigh muscle in the quarter-final victory over Italy and he can play no further part in the tournament, the DFB said.
Juventus midfielder Khedira has a partially torn groin muscle and Manchester United's Schweinsteiger sprained a knee ligament in the penalty shootout win over the Italians on Saturday.
"It is currently in doubt whether Schweinsteiger and Khedira will be able to take any part on Thursday in Marseille or in a possible final in Saint Denis on Sunday," the DFB said in a statement.
Both are receiving intensive medical treatment.
"It's very bitter when important players are ruled out in the decisive phase of a tournament," said Germany's coach Joachim Löw. "I am especially sorry for Mario. He put in some good performances at these Euros and has helped the team, not only with his goals. For us, it means we have to accept the new situation and find solutions, which we will do.
"The quality of the team is high and I have full trust in all the players - we'll be ready on Thursday and we're looking forward to the semi-finals."
After defeating plucky Iceland 5-2, Euro hosts France are looking to avenge their 2014 World Cup elimination.
"It will be a great match, we have a lot of desire to get our own back for the World Cup," French star striker Olivier Giroud said after his two goals helped France thrash Iceland 5-2 in Sunday's quarter-final. The France-Germany semi-final will be on Thursday.
A header from Mats Hummels, who won't be playing Thursday after receiving a second yellow card in during the Italy match, knocked France out in the quarter-final in Rio de Janeiro two years ago and Germany went on to win their fourth global crown.
Arsenal forward Giroud said the showdown with Germany in Marseille will be "a completely different match" to the romp against the Icelanders.
"They are the world champions and they are often in the last four of major tournaments," Giroud said.
"I'm very proud of what this France side is achieving and I hope we'll come out once again with the right result."
Despite Germany's setbacks, France coach Didier Deschamps is in no doubt that Germany are the class act of the tournament.
"Germany are the best team, there is no doubt about that, even if Italy gave them a few scares. But we are there in the final four and we'll give it our all," Deschamps said.
"They are one of the rare teams which can control a match. It will be a great game but it won't be a stroll in the park."