Police, the Scottish Fire and Rescue Service, the coastguard and the RNLI were involved in the search but found no trace of the person despite extensive efforts.
Officers are appealing for information as the search continues on Tuesday.
There is no description of the person or what they were wearing as the incident happened during the hours of darkness.
Sergeant Paul Smith said: “Our search remains ongoing for this person, and we are asking for the public’s assistance to help trace them.
“If you were in the area of the River Tay last night and saw or heard anything that might assist us in our search, please get in touch as soon as possible via 101 quoting incident number 4389 of September 11.”