Defence ministers and leaders from around the world are attending the Shangri-La Dialogue at the hotel.
Police say that the car was stopped early on Sunday morning at a vehicle checkpoint, but accelerated after being asked to open the car boot and rammed through police barricades.
Suspected drugs were found on one of those detained, police said.
Officers opened fire because the car "was endangering the lives of officers", the statement added.
Police say they are in control of the situation.
Extra security is in place due to the conference, which is attended by senior defence leaders including US Secretary of Defence Ashton Carter, who spoke at the summit on Saturday.
Singapore is thought to have one of the lowest crime rates in the world.
The country has tough anti-drug laws, and has enforced capital punishment in some cases of drug trafficking.
Singaporean police say they have killed one man and detained two others near the Shangri-La hotel.