The 22-year-old Träsch twisted his right ankle on Monday night just eight minutes into a Germany XI's 4-0 win over Italian third-division side FC Tyrol in a World Cup warm-up match at their north Italian training camp.
An MRI scan at a hospital in nearby Bolzano, northern Italy, revealed the Stuttgart midfielder has damaged ankle ligaments and cannot train for the next 14 days. The World Cup set to begin on June 11.
Germany's first game is against Australia on June 13 and Löw has now lost two midfielders in just two weeks.
"It was a stupid situation, but it looks as though there is no tear in the ligaments," said Löw after Träsch tripped on the pitch.
With Ballack also ruled out by an ankle injury he sustained playing for Chelsea in England's FA Cup final 10 days ago, Löw has lost yet another midfield option.
Alongside Stuttgart teammate Sami Khedira, Träsch had been an alternative Löw was considering to replace Ballack at the heart of Germany's midfield.
Apart from Bastian Schweinsteiger, Lukas Podolski and Piotr Trochowski, Löw is now lacking experienced midfielders.
Löw must register his final 23-man World Cup squad with FIFA on June 1 and has yet to decide who will captain the side in Ballack's absence and whether Bayern Munich's Hans-Jörg Butt or Schalke's Manuel Neuer will start in goal.
Germany face Australia, Serbia and Ghana in Group D at the World Cup.