The incident took place at about 12.30pm along Bedok North Avenue 4.
The goods vehicle driver reportedly braked abruptly at a traffic junction when the traffic light turned amber.
It was raining at the time, and the goods vehicle skidded due to the wet road conditions, crashed through a pavement barricade and plunged into the roadside drain.
The 57-year-old driver and a 29-year-old passenger were sent to Changi General Hospital.
Police and SBS Transit are investigating the incident.