Glasgow City Council took the decision following health and safety fears over the stability of the roof and the glazing in the gardens.
The Winter Gardens are expected to be closed for a number of weeks following an initial assessment.
No-one was injured in the incident and a full investigation will take place.
Plans have been put in place to re-open the People's Palace museum independently of the Winter Gardens as soon as possible.
A spokesman for Glasgow City Council said: "It is unfortunate that we have had to close the Winter Gardens so unexpectedly but the safety of our staff and the public must be our priority.
"Until we have a more accurate picture of the condition of the structure I'm afraid the Winter Gardens will remain closed. We understand that this is a disappointing situation especially for those who have bookings with the venue and we will make every effort to help find these clients an alternative venue."
The People's Palace museum and Winter Gardens in Glasgow have been closed to the public until further notice after a glass roof panel fell.