Cambridge University student Alana Cutland, 19, fell from the light aircraft after carrying out research in the remote area of Anjajavy on July 25, despite desperate efforts from others on board to keep her inside the plane.
Her body has not yet been recovered.
Ms Cutland's uncle said she had became sick during her time in Madagascar, possibly due to prescription medication.
"She had taken ill after being there for a few days and when she spoke to her mother on the phone two days before the accident she was mumbling and sounded pretty incoherent," Lester Riley, the brother of Ms Cutland's mother Alison, told the Mail Online.
"We think she had suffered a severe reaction to some drugs but not anti-malaria ones because she had taken those on her trip last year to China without any side effects."
The plane's pilot said Ms Cutland had a headache when she boarded and stayed silent during the flight.
"But for the whole time Alana did not say a word - she just struggled to get away from us," Mahefa Tahina Rantoanina told The Sun.
"I have no idea why she opened the door but she did. She opened the door and she jumped. The door did not open itself."
Police photographs recreating Ms Cutland's final moments appear to show the pilot and the second passenger grasping hold of the victim's leg as she hangs out of the plane.
Ms Cutland eventually fell to her death after a tense struggle to free herself.
"The Cessna C168 aircraft was taking off from Anjajavy with three people aboard, including (passenger Ruth) Johnson, Alana and the pilot," local police chief Sinola Nomenjahary told The Sun.
"After 10 minutes of flight, Alana undid her seatbelt and unlocked the right door of the plane and tried to get out.
"Ms Johnson fought for five minutes trying to hold her, but when she was exhausted and out of breath she let go.
"Alana then intentionally fell from an aircraft at 1,130 metres above sea level.
"She dropped into a zone which is full of with carnivorous fossa (a cat-like, mammal endemic to Madagascar)."
It was reported Ms Cutland, from Milton Keynes, suffered "paranoia attacks" while on the research trip to the island, off the east coast of Africa.
Police said she was in regular contact with her parents and was making her way home via the island's main airport.
Family members said the second-year student "grasped every opportunity that was offered to her with enthusiasm and a sense of adventure" and was in Madagascar to complement her studies in natural sciences.
In a statement released through the Foreign Office, her family paid tribute saying: "Our daughter Alana was a bright, independent young woman, who was loved and admired by all those that knew her.
"Alana grasped every opportunity that was offered to her with enthusiasm and a sense of adventure, always seeking to extend her knowledge and experience in the best ways possible.
"She was particularly excited to be embarking on the next stage of her education, on an internship in Madagascar complementing her studies in natural sciences.
"We are heartbroken at the loss of our wonderful, beautiful daughter, who lit up every room she walked in to, and made people smile just by being there."