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."

Nick Alexander, 35, from Weeley in Essex, was killed on 13 November, 2015, at the nightclub in Paris.
Artists including Fran Healy from Travis and Supergrass' Gaz Coombes performed at Shepherd's Bush Empire on Tuesday.
There was also a minute's standing ovation in Nick's honour.
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Mr Alexander was selling band merchandise for Eagles of Death Metal, who were performing at the nightclub, when he was killed.
The concert - called Peaceful Noise -  marked the official launch of the Nick Alexander Memorial Trust, which will provide musical equipment to small charities and vulnerable groups across the country.
Mr Alexander's older sister Zoe, 43, said the event was "really personal" to Mr Alexander and included performances by artists who had toured with her brother or were friends with him.
She said she would remember her brother as someone who "approached life head on".
"He packed a lot into those 35 years so we will remember him in that way - as somebody who embraced life and forged their own path," she said.

Raja Ali's car was rammed and then blocked in at the side by two vehicles in Dagenham on 25 September 2016.
The 33-year-old was then chased and stabbed.
Abubakar Bana, from Hornchurch, Essex, and Jordon Archambie, 20, of Stratford, east London, were convicted following a trial at the Old Bailey.
Daniel Welch, 34, of Winstead Gardens, Dagenham, and Zakar Yunas, 22, of Rokeby Steret, Stratford, were found guilty of violent disorder.
Mussa Jalo, 21, from Norfolk Road, Dagenham, had pleaded guilty to violent disorder at the start of the trial, along with Bana, of Station Lane, and Archambie, of Hesketh Road.
Jurors in the trial heard that Mr Ali was sat in his car along with two friends waiting for what they thought was a drugs deal.
A Mitsubishi Shogun 4x4 then rammed into Mr Ali's car, shunting it forward, while a red Renault Megane pulled up alongside and the occupants got out armed with weapons.
Mr Ali and two other men ran away but they were chased and the 33-year-old was stabbed to death in Braintree Road.
Det Ch Insp Dave Whellams called it a "pre-planned and orchestrated murder".
"Regardless of what Raja's intentions were that night, when he arranged to meet these men he should not have lost his life.
"I hope Raja's grieving family are able to move forward knowing his attackers have now been brought to justice."
All will be sentenced on 3 July.
Cardiff City defender Bruno Ecuele Manga faces at least two months out with a groin injury.
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Hundreds of people have attended a concert held in honour of the only Brit killed in the Bataclan terror attack a year ago.
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Two men have been found guilty of the manslaughter of a drug dealer who was stabbed to death after being ambushed by a rival gang.