Duncan wrote to Mayor Boris Johnson as well as speaking to the Architect's Journal about the bridge, which is intended to span the Thames from the South Bank to Temple, just east of Waterloo Bridge.
The AJ has carried out a long-running investigation into the contracts and public funding of the pedestrian bridge, alleging discrepancies in the procurement design process as well as questions over the amount of public funding which has been allocated to its construction.
The Mayor's office has called the procurement process for the bridge "open, fair and transparent", echoing a Transport for London audit last year which concluded procurement had been fair and transparent.
Duncan said: "The allegations relating to the procurement of the Garden Bridge are extremely concerning. All those who bid for work have a right to expect that their submissions will be judged fairly, transparently and in accordance with the law.
"Given the high profile nature of this project, the amount of public money at stake and the seriousness of the allegations, we would urge that the project is put on hold and the whole procurement process is then opened up to detailed scrutiny."
She added that this was in no way a comment on the work of the "immensely talented" Heatherwick Studio and Arup teams, which won respectively the design and engineering contracts for the bridge.
"Our concerns are about the fairness and transparency of the procurement process."
Len Duvall, leader of the London Assembly Labour group, said the assembly would be pushing the mayor for "full disclosure" about the procurement process.