N Srinivasan recently stood down temporarily as chief of the Board of Control for Cricket in India (BCCI) following a Supreme Court ruling.
He owns a team in the IPL, the world's richest cricket tournament.
He is regarded as the world's most powerful cricket administrator.
He was elected chairman of cricket's world governing body, the International Cricket Council, in February and is due to take up the role in July.
Last month, former India captain and batting legend Sunil Gavaskar was installed as the interim head of the cricket board.
The Supreme Court said on Wednesday that the BCCI should appoint a panel to investigate the charges against Mr Srinivasan and 12 others, including some players.
"Having come to know the nature of allegations, we cannot close our eyes," the court said.
The court said when the allegations of corruption in IPL "were brought to his [Mr Srinivasan's] notice... he did not take any action. That means he was aware about the allegations and did not take it seriously".
The seventh edition of the 20-over tournament, which features eight teams, begins on Wednesday and runs until  1 June.
The last season of the IPL was dogged by allegations of spot-fixing and betting.
Spot-fixing involves players bowling wides and no-balls at certain times arranged beforehand with bookmakers.
Mr Srinivasan had "stepped aside" from his post as BCCI president in June last year after his son-in-law Gurunath Meiyappan was arrested over allegations of betting.
Mr Meiyappan was later freed on bail, and Mr Srinivasan returned as the head of the cricket board before he was asked to leave his post. Both men deny any wrongdoing.
The IPL is considered to be the world's showcase for Twenty20 cricket. Top Indian and international players take part, contributing to what is the world's richest cricket tournament.
India's Supreme Court has asked the cricket board to investigate the role of a top cricket official and 12 others in spot-fixing and illegal betting in the Indian Premier League.