The closure of the Millennium Bridge will enable the replacement of a layer which separates its steel structure from its aluminium deck, the footbridge’s owners, City Bridge Foundation, said.
Round-the-clock work to complete the repair will begin when the bridge shuts on October 14, for what is believed to be at least its fourth closure.
It quickly earned the "wobbly bridge" nickname because of the alarming way it swayed and vibrated when large numbers of people crossed it.
The bridge was closed for repairs days later, reopening in 2002 after shock-absorbers were fitted to reduce movement.
The new issue is reportedly unrelated to the previous wobbling problem.
City Bridge Foundation chairman Giles Shilson said the well-used crossing, which opened to mark the new millennium, is "starting to show its age".
He said: "The separation layer under the bridge deck has started to degrade, which means it's having an adverse effect on the bridge deck and needs addressing urgently.
"Replacing this layer is a time-consuming process, meaning we have no option but to close the bridge for three weeks and to work round the clock to get it done as quickly as possible.
"We're sorry for any inconvenience but hope people will understand we do need to do this work, and will see the benefits after we give the bridge a much-needed deep clean that will leave it looking as good as new."
The bridge is to close at 8am on October 14 and reopen on November 5. Pedestrians will be diverted to other routes that take them over Southwark Bridge and Blackfriars Bridge.