Pedestrians had to wait for half an hour before they were able to continue crossing the bridge.
Engineers made safety checks to the structure after it was forced to close briefly. A limit was subsequently imposed on the number of pedestrians allowed to cross the bridge.
A spokeswoman for the Millennium Bridge Trust said the swaying resulted from about 100,000 people crossing the span.
"We anticipated 10,000 people, but we think we had about 100,000 over the bridge. The bridge is 100% safe, it's just that it does move when there are such large numbers of people crossing it.
"We are satisfied we have now come up with a system to deal with these crowds if they occur again. We will have someone down at the bridge tomorrow to monitor the crowds."
A City of London police spokesman said: "From what I have gathered anybody who was a bit unsteady on their feet might have been in trouble."
"It was swaying in the wind and we closed it while we got in touch with the bridge's engineers and city engineers to see if it was safe," he said.
Designed to sway
A spokesman for architects Foster and Partners who designed the bridge with engineers Ove Arup and Partners said: "Because there was such a huge number walking all at once across the bridge, which is very unusual, there was a certain amount of swaying.
"The bridge is intended to have some movement. It's a suspension bridge - if there isn't movement there can be a problem."
Pedestrians had to wait for half an hour before they were able to continue crossing the bridge.
Those who had made it across before the closure said they had been surprised by the swaying sensation.
Margaret Vint, 60, from Burnham, Buckinghamshire, said: "I think you need to take your sea sickness pills before crossing.
"The vibration was tremendous - I could feel the whole weight of the bridge swaying.
The closure, albeit temporary, was another embarrassment for a high-profile venture in London.
The Millennium Dome at Greenwich has had negative publicity since it opened, while the opening of the Millennium Wheel near Westminster was also delayed for a time, although it is now considered a success.
Earlier, celebrities joined charity fund-raisers to be first to cross the Millennium Footbridge, which links St Paul's Cathedral to the new Tate Modern art gallery.
'Blade of light'
Former model Heather Mills led a party of school pupils who were among 6,000 people on a sponsored walk in aid of Save the Children.
Miss Mills was joined by H from pop group Steps, TV news presenter Julia Somerville and Coronation Street actor Chris Bisson.
The project cost over £18m and was designed by architect Sir Norman Foster and the British sculptor Sir Anthony Caro.
The bridge is intended to look particularly striking when lit up at night. Sir Norman said it would form a "blade of light" across the Thames.
Over half the money for the bridge has come from Lottery funds. The Millennium Commission contributed over £7.1m and the Corporation of London gave a further £3.5m.
The project is reported to have exceeded its budget by over £2m.
It was inaugurated by the Queen last month, but at the time had not been completed. It had originally been intended that it would open to coincide with the opening of the Tate Modern.
At the official dedication ceremony, London mayor Ken Livingstone said: "It will be so good to actually walk across the river peacefully, without cars and trains thundering by."