Traesch, who was injured in a friendly against South Tirol at their training camp in Italy, was the third player to be ruled out of the June 11-July 11 tournament in South Africa after captain Michael Ballack and starting keeper Rene Adler.
"No, there will not be another nomination," Flick told reporters from the team's training base in northern Italy.
"There are several options, though they have narrowed down a bit. Dennis Aogo has played that position as has Heiko Westermann," he added referring to left-sided defender Aogo and central defender Westermann.
VfB Stuttgart's Traesch, 22, has two caps and was a candidate for the midfield spot left vacant by Ballack, who was ruled out of the World Cup after being injured in the English FA Cup final 10 days ago.
Traesch will be sidelined for about six weeks.
"If you compete in such a tournament you have to have a certain degree of flexibility as a team," Flick said.
The preliminary Germany squad has now been narrowed down to 25 players, which must be reduced to 23 by June 1st.
"With Rene Adler, Michael Ballack and Christian Traesch there are three players who would have been in that 23-man squad. I think we have been punished enough and that all will be fine from now on," said Flick.
"As a coach you cannot choose when the injuries will occur. We have to live with that," he added. "We have a large group and players who can play various positions."
Germany have been drawn with Serbia, Australia and Ghana in the group stage.
