The three mopeds were travelling south on the bridge when they mounted the east pavement and hit the woman at about 00:40 BST.
City of London Police said they had tried to stop the group in Gracechurch Street but lost sight of them.
The woman was taken to hospital where she was treated for a leg injury.
A spokesperson for the force said officers were not pursuing the gang along the bridge at the time but had been monitoring them on CCTV.
"The City of London Police is investigating this incident and anyone with information is asked to contact 101," the force said.
Security barriers were installed alongside the pavements on London Bridge following June's terror attack.
A pedestrian was knocked down by a moped gang riding along the pavement on London Bridge after police had earlier tried to stop them.