"If it is established that he did it, we cannot say he will be let off," additional police commissioner Deependra Pathak told AFP as the interrogation started on Thursday.
The 32-year-old faced "comprehensive" questioning that would cover "all angles of the case," Pathak said. "A criminal case has been registered here and it must meet its logical end."
Gibbs had admitted accepting money from disgraced former captain Hansie Cronje to score fewer than 20 runs against India in a one-dayer during a 2000 March-April tour.
He subsequently scored 74 runs and said he had "forgotten" about the deal, but was suspended and fined by the South African authorities.
Pathak noted that the South African inquiry findings were "not enforceable in India."
The questioning at police headquarters in New Delhi would focus "specifically on whether he took money in cash or through a bank transfer from an Indian bookie based in London or another bookmaker," a senior police official said.
If Gibbs took money, that would "construe an illegal offence," said the official.
India was shaken by a betting scandal that rocked the national team in the late 1990s, the official said.
The South African, who has played 79 Tests and is in India for the Champions Trophy cricket tournament, was accompanied by two lawyers and a diplomat.
Crime Branch joint police commissioner Ranjit Narayan led a team of detectives in the interrogation.
Gibbs has previously refused to tour India since 2000 after failing to obtain assurances he would not be detained.
Implicated in the same scandal was Cronje, who admitted involvement and was served with a life ban before dying in a plane crash in 2002.
South Africa, winners of the maiden Champions Trophy in 1998 in Bangladesh, are scheduled to play their first match against New Zealand in Mumbai on Monday.
The International Cricket Council in May said it would do everything possible to ensure Gibbs could tour India without fear of arrest in the match-fixing case.