Muhammad Syahid Mohamed Yasin and Mohamed Ismail, both Singaporeans, were accused of possessing about nine grams of powdery substances believed to be heroin for the purpose of trafficking.
Yasin, 26, was remanded for a week and could be taken out for investigations. The prosecution said he might be charged with other offences.
Ismail, 31, faces the same charge. As he was injured in the incident, he was charged in the Singapore General Hospital via video link.
The two men were arrested at about 4.30 am yesterday. They were in a car with 34-year-old Mohamed Taufik Zahar when they were stopped at a police checkpoint near Shangri-La Hotel, where the high-level Shangri-La Dialogue summit was taking place.
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Mohamed Taufik, the driver, suddenly accelerated and crashed the car through police barricades, endangering the lives of the officers on duty at the security check point.
Police opened fire at the vehicle, which stopped at the junction of Orange Grove Road and Anderson Road around the hotel.
The Shangri-La Dialogue - which was attended by defence ministers and military chiefs from around the world - was not affected by the incident.