nuTonomy, the firm behind the scheme, said the car had clipped a small lorry while driving at about four miles per hour.
It played down the incident as a "small prang", saying only minor damage was caused and that neither of the two engineers on board were hurt.
The Singapore scheme, which began in August, was the first around the world trialling driverless taxis.
The nuTonomy spokesperson said that given this was a trial, small accidents were not unexpected and that the idea of the testing was to learn from what went wrong.
The project is using six small Renault and Mitsubishi electric vehicles, equipped with the company's software and cameras. Each has a system of lasers which operate like a radar to monitor the car's surroundings.
But while the vehicles are doing the driving themselves in a small area of the city, drivers are there to monitor the performance and as a backup in case something goes wrong. Currently the vehicles are not taking paying passengers.
Driverless technology is one of the biggest growth areas in the automotive industry and just about every car company is working on driverless technology from Silicon Valley's Tesla to Ford, Volvo, BMW and a number of Chinese car makers.
Internet giant Google was amongst the first to pioneer and extensively test its driverless Google car and has teamed up with a number of car makers for their research.
nuTonomy, is a US-based start-up developer of software for self-driving cars. The company was founded in 2013 by two MIT researchers specialising in robotics and driverless technology. The firm has offices both in the US and in Singapore.
A self-driving taxi being trialled in Singapore has had its first accident.