The £5m signing from Lorient sustained the grade-three tear on international duty with Gabon.
Bluebirds boss Russell Slade is seeking clarification on how last season's player of the year suffered the blow during training between games.
"It is very difficult with Gabon to request what they have done and find out what they have done," said Slade.
"Training regimes are different. We could help them if we could get information on how they prepare and how they train as well.
"It's very important and we don't seem to get any dialogue from them.
"Obviously the medical  department and myself would like to know because it s out of our control what they are doing in the meantime."
Cardiff hope Ecuele Manga's fellow centre-back Ben Turner will be able to return from ankle surgery in an under-21 game on 13 November.
Meanwhile, Bluebirds captain and goalkeeper David Marshall is expected to return for Saturday's Championship clash at Preston after serving a two-match ban after a red card at Rotherham. Simon Moore has been deputising.
"When you break it down, Preston seem to be finding life a little bit tougher at home. Hopefully that continues for at least one more week," said Slade.
"Simon [Grayson] is a good manager, who has had several promotions to the Championship with various teams, so he knows his way around.
"He will set his team up to be very difficult. It has not quite happened for them at home yet but I am sure they will be more than capable of climbing the table in the coming weeks."
Cardiff City defender Bruno Ecuele Manga faces at least two months out with a groin injury.