A police statement said the disturbance started in the congested Little India district when one person was killed after being hit by a bus. The victim's identity was not immediately disclosed.
About 400 people on the scene began attacking police vehicles after officers responded to the accident.
Pictures and videos on social media showed at least two vehicles including an ambulance on fire, while two police vehicles were seen being overturned by a cheering mob.
The situation was brought under control after the elite Special Operations Command and Gurkhas working for the police arrived on the scene.
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Teo Chee Hean, the deputy prime minister and minister of home affairs, said in a statement that "this is a serious incident which has resulted in injuries and damage to public property."
"The situation is now under control. Police will spare no efforts to apprehend the subjects involved in the riot."
Many congregate in Little India on Sundays to shop, dine and drink.