"Somewhere down the line franchises need to control these things. A certain player from a certain team does these things, the franchise needs to be fined and it has to be fined heavily," Gambhir said.
Royal Challengers Bangalore's Luke Pomersbach was accused of molestation by an American national during the just- concluded fifth edition of the Indian Premier League.
Gambhir, who captained Kolkata Knight Riders to their maiden triumph on Sunday, defended the BCCI and IPL as far as preventing players from getting embroiled in off-field controversies are concerned.
"It is the responsibility of the franchise to control its players. BCCI can't appoint one person each to keep a watch over every player," Gambhir told 'Headlines Today'.
"Players who have a history of binge drinking and have got into trouble in the past, franchises should impose a curfew on them and they should be sent back to their rooms."
The IPL also faced allegations of spot fixing and black money leading BJP MP Kirti Azad to demand a ban on the league.
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"We keep blaming the BCCI and the IPL for all these things. A lot of these things can be sorted out if the franchise is strong enough. Whatever we sign for is given, and nothing is given under the table."
Answering the parliamentarians' demand for a ban, Gambhir said, "I am sure there are a number of other issues for parliament to debate than the IPL."
Gambhir also said that his effort was to make KKR be known for its on-field achievements.
"In the last three years, KKR has been known too much for what happened off the cricket field. I wanted to change that.
"The one thing I cannot do is dance for SRK. SRK has succeeded in everything, the only thing he has failed to do is make me dance. And I hope he will not try again."