At 2am on Thursday, Bowon Mongkol police contacted a rescue team to help find the missing couple.
They assigned two teams of divers to search for the bodies for one-and-a-half hour but there was no sign of the victims.
The police examined a bag that was left behind and found no identification inside, only female clothing.
Witnesses said they saw a female Muslim woman sitting in a park under the bridge and later walking over to the pier with a man. A short moment later, they were heard screaming for help in the river.
The witnesses said they called the police and threw objects into the river for the victims to grab on to but the current was too strong and the helpless couple disappeared under the surface.
The divers had momentarily halted their search operation because of the strong water current. They believe this must have swept the two away from the spot they were last seen in.