Alana Cutland, 19, died earlier this month on the island off the east coast of Africa in the Indian Ocean.
Local media reports suggest Ms Cutland, from Milton Keynes, fell from a light aircraft after carrying out research in the remote area of Anjajavy last Thursday.
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.
"She was always so kind and supportive to her family and friends, which resulted in her having a very special connection with a wide network of people from all walks of her life, who we know will miss her dearly.
"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.
"Alana was also a talented dancer and embraced the more creative side of her talents with joy and commitment.
"Her thirst for discovering more of the world always ensured she made the most of every second of her action-packed young life.
"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."
Dr David Woodman, of Robinson College, Cambridge University, said in a statement: "Robinson College is deeply shocked by the news of Alana's death. In her two years here, she made a huge contribution to many different aspects of life in the college.
"She will be sorely missed by us all. The college extends its sincerest condolences to Alana's family at this extremely difficult time."
Ms Cutland was involved in the yoga and mindfulness society at the college, according to its website.
The internship is understood to have been undertaken privately and was not a Cambridge University study trip.