The hub is having a new boiler fitted and given it will be without hot water, the facility will close to the public.
The work starts on Monday October 5 and staff will be transferred to other hubs.
The nursery that uses the building has a separate boiler and will remain open.
Cllr Mieka Smiles, Executive Member for Communities and Education, said: "It's a shame we have to close the hub for a short while, but the new boiler is essential and we can't run the building safely with no hot water.
"We look forward to welcoming people back very soon."
Residents are welcome to use other hubs around the town and the Council also offers free access to downloadable eBooks and audiobooks via Borrowbox.
More information is available here: https://www.middlesbrough.gov.uk/leisure-events-libraries-and-hubs/community-hubs-and-libraries/elibrary