Striker Gomez, who had scored twice and is the team's only out-and-out striker, tore muscle fibre in his right thigh on Saturday, a medical check revealed on Sunday.
Khedira, who also missed their winning 2014 World Cup final through injury, was taken off in the 16th minute after overstretching during a challenge for the ball in Germany's 6-5 victory on penalties over the Italians.
The 29-year-old had played in every match of the tournament so far as Germany eye a fourth continental title but like captain Schweinsteiger he is doubtful for the rest of the tournament in France.
Khedira suffered an adductor muscle injury while Schweinsteiger stretched a ligament in his right knee.
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"It is very bitter when you lose key players at the crucial phase of a tournament," said Germany coach Joachim Loew.
The Germans have conceded only one goal in regular playing time in five matches and on Thursday will face either hosts France or Iceland, who were playing later on Sunday.
"I am especially sorry for Mario who played a great tournament and helped the team not just with goals," Loew said.
"This means we will have to face a new situation and find solutions. The quality of the squad is high and I have full confidence in my players."Germany will also be without suspended central defender Mats Hummels who was ruled out of the semi-final with a second yellow card on Saturday.
(Reporting by Karolos Grohmann; Editing by Clare Fallon)
