Ten classrooms and the library have been damaged - repair work needs to be carried out to the roof.
The electricity supply to significant parts of the building has been turned off.
In a letter to parents Headteacher Jeff Bird says: 'We have reluctantly taken the decision to close Bishopston Comprehensive school for the rest of this week.
'We would like to apologise for the inconvenience this is going to cause but rest assured we are doing all we can to resolve the issues as quickly as possible with the aim or re-opening next week.
'We will be updating our social media channels and website to keep you informed.'