She had become very ill, and was rather old for a possum, so got put to sleep by vets at the Leipzig Zoo.
Heidi became a global megastar when photos of her appeared in a German newspaper.
A song was written about her, she appeared on TV shows and a stuffed Heidi toy was made.
Heidi was found abandoned outside an animal shelter in America in 2010 and was moved to Leipzig Zoo in Germany.
The problem with her eyes was caused by a poor diet and excess fat behind her eyeballs.
Her death is sad news for her huge number of fans. More than 300,000 people had become friends with her online.
This has been a bad week for celebrity animals starting with ‘H’with news that Hope the Black Bear had been shot in Minnesota.