Moras, a regular starter in recent months having formed an effective partnership with Greece's other "Twin Tower" Socratis Papastathopoulos, has not trained in the past few days and was expected to continue receiving medical treatment on Tuesday.
"He is very unlikely to play against South Korea unless there is a last-minute medical wonder," the team official said.
The defensive gap will most likely be filled by experienced all-rounder Kostas Katsouranis who will move from his usual midfield position, as he did in training on Monday.
Striker Pantelis Kapetanos will also skip training on Tuesday as he tries to get over a minor knock but, like defender Sotiris Kyrgiakos, who trained separately on Monday, is expected to be fit for the match in Port Elizabeth.
Greece, in only their second World Cup, also take on Nigeria and Argentina in Group B.