Mr Bell said it was not known just how long the pedestrian-only structure will have to remain shut. It is thought the closure could last for weeks.
The closure of the 320-metre long cross-Thames structure in central London just two days after its public opening was "a big, big disappointment", added Millennium Bridge Trust chief David Bell.
But he said: "We have been overwhelmed by how many people have said they love the bridge."
Mr Bell said it was not known just how long the pedestrian-only structure will have to remain shut. It is thought the closure could last for weeks.
The trust has already received £7.1m of National Lottery money to help finance the bridge which runs from St Paul's Cathedral north of the Thames to the Tate Modern at Southwark on the south bank.
Mr Bell said: "I am confident we can raise the money for the repairs but I don't know if we will go back to the Millennium Commission to ask for funds or not.
"Officially inaugurated by the Queen last month, the bridge officially opened to the public on Saturday with a celebrity sponsored walk.
But with thousands of people attending the opening, the bridge swayed so much that it had to be closed for 10 minutes and numbers on it after that were limited.
With a team from the bridge's engineers, Arup, inspecting the structure, a decision was finally taken to close it to the public from 10pm on Monday night.
Millennium jinx
Mr Bell said: "The engineers are doing a whole series of tests to try to understand why this unusual movement took place. They have to try to make the bridge do what it did on Saturday so they can fully assess the problem. It could take them a week to come up with the cause.
Mr Bell went on: "We are so disappointed. This is the last thing we expected or wanted to happen."
Millennium projects appear jinxed.
The £758m Millennium Dome has endured a cash and visitor crisis which has led to the ousting of both its chairman and chief executive.
And the opening of the Millennium Wheel, officially known as the British Airways London Eye, had to be postponed after a problem with the clutches on the passenger capsules.