In September, the firm confirmed it was in the early stages of assessing an offer for the Premier League club.
But in a statement issued to the London Stock Exchange, the company said it had "terminated" its interest in a takeover bid and was "no longer considering making an offer".
Cain Hoy had until 10 October to firm up its interest or withdraw it.
Spurs are currently trying to finance a project to construct a new 56,250-capacity stadium.
When Cain Hoy confirmed their interest in a Tottenham takeover on 12 September, without the club's consent, Spurs swiftly issued a statement saying they had met company representatives but added there were "no ongoing discussions".
Instead, the club said it was focused on the new stadium development and the season ahead.
When contacted by BBC Sport regarding Cain Hoy's withdrawal of interest, the club said it had nothing further to add.
Cain Hoy's latest statement, however, did leave open the prospect of the company renewing its interest after a six-month restriction, which comes into place with immediate effect in accordance with the City Code on Takeovers and Mergers.
Tottenham plan to move out of their White Hart Lane stadium by 2017, but a legal wrangle means they will have to find a temporary home venue for the 2017-18 season.
But West Ham would likely block any move from Spurs to ground-share at the Olympic Stadium, according to Hammers' vice-chairman Karren Brady.
Other potential ground-shares include Wembley and Stadium MK in Milton Keynes.

The University of Southampton team looked at available medical studies and found evidence the two were linked.
But there was no proof that one necessarily caused the other.
It may be that people taking anti-depressants put on weight which, in turn, increases their diabetes risk, the team told Diabetes Care journal.
Or the drugs themselves may interfere with blood sugar control.
Their analysis of 22 studies involving thousands of patients on anti-depressants could not single out any class of drug or type of person as high risk.
Prof Richard Holt and colleagues say more research is needed to investigate what factors lie behind the findings.
And they say doctors should keep a closer check for early warning signs of diabetes in patients who have been prescribed these drugs.
With 46 million anti-depressant prescriptions a year in the UK, this potential increased risk is worrying, they say.
Prof Holt said: "Some of this may be coincidence but there's a signal that people who are being treated with anti-depressants then have an increased risk of going on to develop diabetes.
"We need to think about screening and look at means to reduce that risk."
Diabetes is easy to diagnose with a blood test, and Prof Holt says this ought to be part of a doctor's consultation.
"Diabetes is potentially preventable by changing your diet and being more physically active.
"Physical activity is also good for your mental health so there's a double reason to be thinking about lifestyle changes."
Around three million people in the UK are thought to have diabetes, with most cases being type 2.
Dr Matthew Hobbs of Diabetes UK, said: "These findings fall short of being strong evidence that taking anti-depressants directly increases risk of type 2 diabetes. In this review, even the studies that did suggest a link showed only a small effect and just because two things tend to occur together, it doesn't necessarily mean that one is causing the other.
"But what is clear is that some anti-depressants lead to weight gain and that putting on weight increases risk of type 2 diabetes. Anyone who is currently taking, or considering taking, anti-depressants and is concerned about this should discuss their concerns with their GP."
American investment company Cain Hoy has said it is no longer considering making an offer to buy Tottenham.
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People prescribed anti-depressants should be aware they could be at increased risk of type 2 diabetes, say UK researchers.