The 2003 and 2007 champions open their World Cup, co-hosted by New Zealand and Australia, against Morocco in Melbourne.
Germany also face Colombia and South Korea in Group H.
Hegering is the cornerstone of the German defence but is struggling with an ankle injury, while midfield dynamo Oberdorf has a thigh strain.
"It looks like we won't be able to rely on either of them in the first match," said Germany coach Martina Voss-Tecklenburg.
Hegering and Oberdorf, who both play for Champions League finalists Wolfsburg, were key members of the Germany team beaten by England in the Euro 2022 final at Wembley.
They are likely to be replaced by Chelsea players Sjoeke Nuesken and Melanie Leupolz against World Cup debutants Morocco.
Germany lost 3-2 at home to Zambia in a warm-up friendly a fortnight ago, a shock defeat which defender Kathrin Hendrich described as "definitely a wake-up call".
Despite having Hegering and Oberdorf missing for the first game, Voss-Tecklenburg believes Germany can challenge for the World Cup.
"We're right on schedule and we don't have any jet lag issues anymore," she added.
"We want to compete for titles.
"We've stoked expectations. We won't succeed in everything, but we promise there will be passion and intensity.
"We will go to - and beyond - our limits."
