Two footballers apologised after being photographed apparently urinating into a glass at last year's festival, where women were seen baring their breasts.
Chief executive Ian Renton said: "It's to ensure that drinking is not the rationale for people coming racing."
The measure is also to be imposed at the Jockey Club's other racecourses.
It comes in first at Cheltenham, where the festival takes place next month, but will be in place at Epsom, which stages the Derby, and Aintree, where the Grand National is held.
"It's an improvement on things we are already doing," Mr Renton said.
"Aintree has already got the ball rolling, with their Ladies' Day, they've already taken steps to improve the way that is perceived.
"We want them to come to racing and enjoy the sport and not have those people coming who will be a nuisance to other racegoers," added Mr Renton.
As well as the four-drink limit, corporate complimentary bars will close earlier and water points will be made available in every public bar.

The lender, which recently announced a pre-tax loss of Â£37.3m in 2014, said the new ads would steer clear of the young and vulnerable.
But it admitted there would be no watershed for TV adverts, which will run during ad breaks of popular soaps.
The payday lender's website has also been overhauled.
Applicants applying for short-term loans on the site would see clearer affordability warnings, details of costs if repayments were missed, more prominent links to debt charities, and a new logo, the company said.
Wonga's adverts featuring puppets were cut in July last year, with the company saying it did not want to be associated with "anything which inadvertently attracts children".
It is returning with new TV and digital adverts, starting on Tuesday, featuring farmers to dental nurses, who it believes are among a broader group of target customers. The average customer for a Wonga loan at present is male and aged between 20 and 35.
"It is clear that the puppets were inappropriate," said Tara Kneafsey, UK chief executive of Wonga.
Wonga has had to apologise and compensate customers for the use of letters from fake legal firms, as well as write off unsuitable loans. Ms Kneafsey said the new adverts did not contain a further apology, as they aimed to show how the company had moved on.
The lender estimates there are 13 million people in the UK who are struggling with money and are turned down by mainstream lenders. This also includes people who are new to the credit market, such as those moving into the country.
It said adverts would not be shown on children's TV, or channels or programmes with a large audience among younger people. Billboards within 50m of a school or college would also not be used for poster adverts.
Wonga also sponsors Newcastle United football club, but has agreed to remove its logo from all children's replica shirts from the 2016-17 season.
The company, along with other payday lenders, now faces new rules from the regulator, the Financial Conduct Authority (FCA), which ruled that customers must face stricter affordability checks.
The regulator's main weapon is a cap on the cost of payday loans of 0.8% of the amount borrowed per day, which came into force in January. As a result, Wonga's payday loan APR has dropped from 5,853% to 1,509%.
This has already cut the size of the payday lending industry in the UK. Wonga is among those that has seen a big drop in customers and expects to continue making a loss in 2015.
It said it had now introduced a series of safety net measures for customers, including a three-day grace period for late repayments before a default fee was charged, a money-back guarantee for customers who change their minds on loan applications within 24 hours, and a worst-case scenario box on the cost of a loan.
It admitted it had "lost its way" under the previous management regime and had considered dropping the Wonga brand.
While the Wonga name will be retained for the payday loan, other longer-term, larger loans expected to be launched later in the year could be advertised under a different name.
Chris Bibby, marketing and brand director at Wonga, said it would have been "wrong to whitewash it and pretend to be someone else".
Cheltenham Festival racegoers will be restricted to buying four alcoholic drinks at a time in a bid to crack down on anti-social antics.
[NEXT_CONCEPT]
Short-term lender Wonga has swapped its controversial puppets for "hard-working dinner ladies and mums" as it bids to reinvent itself with new adverts.