The city council says repairs to high level glazing in the glass house, costing £140,000, needs to be carried out ahead of the Commonwealth Games.
Work will start on October 1 and will result in the attractions being temporarily closed from Mondays to Fridays.
It is hoped - weather permitting - the work will be finished by mid November.
The progress of the work will dictate whether the Winter Gardens and People's Palace can remain open at weekends.
Alistair Watson, the council's land and environment spokesman, said: "The Winter Gardens are a much loved part of Glasgow and we are dedicated to improving the facility.
"The significant investment we're putting in will prepare the Winter Gardens for the year of the Commonwealth Games.
"In order to carry out the works as quickly as possible and minimise disruption, the People's Palace and Winter Gardens will be closed during the week and reopen at weekends.
"As always, we need to bear in mind the Scottish weather. Should works fall behind due to unfavourable weather, there maybe a requirement to work weekends and the potential resultant short notice closure. Obviously, all reasonable steps will be taken to avoid this."
The People's Palace is Glasgow's social history museum. It was opened in 1898 and gives visitors a chance to see the story of the people and city from 1750 to the present.
The Winter Gardens, is an elegant, iron-framed Victorian glasshouse. A popular hire venue for private functions, the latest refurbishment will ensure it can continue to serve the city as a warm, and dry, entertainment venue