Former Test bowler Shanthakumaran Sreesanth and two other players were arrested along with 11 bookmakers on Thursday on suspicion of spot-fixing in the Indian Premier League.
The case has prompted the Indian government to look at the possibility of introducing a law to combat matchfixing and spot-fixing.
Cricket fan and social activist Sudarsh Awasti lodged the petition demanding the scrapping of the remaining four IPL matches, including Sunday's final, but the apex court said the competition would go on as scheduled.
The court also asked the Indian cricket board to submit a report within two weeks with details of the players' involvement in the scandal and what action is being taken against them.
Cricket is a gentlemen's game and it should remain so, the court observed.
Awasti also wanted a special investigation to get to the bottom of the spot-fixing scandal and for the league to be banned from next year, but the court found no merit in his demands.
India's film industry was also pulled into the controversy when Mumbai Police arrested a Bollywood actor, Vindu Dara Singh, on Tuesday for alleged links to a bookmaker.
"Mr Vindu Dara Singh has been arrested ... He was in contact with some bookie, that's what I can tell you right now," a senior police officer, Satyanarayan Chaudhury, told Reuters, refusing to disclose further details.
Legal sports betting in India is confined to horse racing, while illegal betting syndicates thrive in the absence of a law dealing specifically with such corruption in sport.
Media estimates put the amount gambled on India's top cricket Twenty20 competition at $427 million (£281m) in 2009.