Although no one was injured, police had to cordon off the building for around three hours while health and safety officers looked into the cause of the plunge.
Following an investigation, it emerged that the glass had been dislodged by a sky platform which snagged on a piece of protective plastic in strong winds.
It is the second time in less than six months that Birmingham's city centre has had to be closed because of falling building material from key 'iconic' construction projects.
In December last year, roads were shut off when five pieces of metal cladding plummeted from near the top of Ian Simpson's 39-storey Beetham Tower ( Cladding falls from Simpson's Beetham Tower
The Howells scheme, which is being developed with Urban Splash, will see the famous concrete tower converted into 234 luxury apartments and features a full recladding of the entire facade.
Explaining what had gone wrong, Guy Jackson, the West Midlands director of Urban Splash, said: '[One] of the HSE-approved sky platforms being used on the Rotunda caught on a piece of protective plastic, due to high winds.
'This resulted in the dislodging of a small piece of framework and the breaking of part of a pane of glass, which fell into Rotunda Square.'
He added: 'Our first and foremost priority is the safety of the public and our workers. Upon the incident happening, we acted immediately, with all work stopping on the sky platforms.
'We are now reviewing the operation of the sky platforms with the HSE to ensure the method is failsafe,' he added.