No one was injured in the incident that took place around 5.15pm.
The flight of stairs had been constructed by the Darjeeling municipality around a year ago.
A shopping complex is being built along the stairs and local people alleged that the contractors had been digging up underneath the staircase that led to the subsidence.
Amar Singh Rai, the chairman, Darjeeling municipality, said: "The municipality engineers are preparing a technical report and we will file an FIR against the builders based on the findings of the report. The municipality engineers will look into any deviation from the proposed building plan and other details."