Yogvitam Pravin Dhokia, 27, was arrested by police for a rash act after he found his way onto the track in the Marina Bay Street Circuit on Sunday, the Channel News Asia reported.
According to the charge sheet, Dhokia's rash act on Sunday night "endangered personal safety of the drivers".
He was charged under Section 336(a) of the Penal Code, Chapter 224. Bail was set at 15,000 dollars and his passport was impounded.
The judge acceded to his request to make a phone call to an unknown party.
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CCTV footage released hours after the race showed him entering via a gap in the fence.
Clad in a T-shirt and shorts, Dhokia then crossed the track and walked against the flow of traffic before climbing back over the barrier.
His actions caused the safety car to be deployed and at least one driver, runner-up Daniel Ricciardo of Red Bull, said the man's intrusion affected the outcome of the race, according to the report.
Race organisers Singapore Grand Prix are expected to submit a full report of the incident to the Federation Internationale De L'Automobile (FIA), motorsport's world governing body.
Dhokia is currently in remand. The case is adjourned for two weeks and the next hearing will be October 6.
Fresh charges may be brought against him, the report added.