The Dane left Wednesday's game against Portugal with an injury, and has now been ruled out of his side's final group encounter versus Joachim Low's team.
The 33-year-old attacker was taken off on the hour mark during the 3-2 loss to Portugal on Wednesday evening with a suspected hamstring problem.
Niki Zimling, who has been nursing a toe injury since the tournament began, could be fit to play, however.
"There is no chance with Rommedahl. Zimling I can still hope for," Olsen told reporters.
The severity of the Brondby forward's injury remains unknown for now as he will undergo tests to determine the length of his recovery, and whether he can continue in the championship should the Danes advance to the knockout phase.
Denmark will seal progression to the quarterfinals if it beats Germany and Portugal fails pick up three points against Netherlands. Kickoff for both clashes on June 17 is at 2:45 p.m. ET.
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